1. Additional Changes to Parameters

The latest "Parameters" spreadsheet (21 Sept) contains two kinds of changes. First come adjustments to a few variable definitions, shown below and highlighted in gray. Second comes the promised completion of the logistic function parameters, which are highlighted in light blue.

The following changes to variable definitions stem from reflection on the variables as I worked through the trustee evaluation score. Additional minor changes have been made on the spreadsheet and highlighted in gray.

1.1 Doctoral students per regular faculty member has been added to the definition of "Departmental academic standing," and the weights adjusted to accommodate. The definition of doctoral talent has been adjusted to equal zero if there are no doctoral students. Corrects omissions.

1.2 Definition of faculty salary/peer-institution faculty salaries in the "Faculty satisfaction index" has been clarified to show that the comparison is with the peer salary in the person’s age-rank category. The calculation of peer salaries is described in a later section.

1.3 Average student diversity (over all student levels) has been added to the definition of the "Faculty satisfaction index." Faculty care about student diversity. The weights have been adjusted to accommodate the new variable, and to reflect concern by non-minority as well minority faculty. (Minority faculty place a greater weight on diversity, however.)

1.4 Faculty diversity has been added to the "Student overall satisfaction" definition for traditional undergraduates. The weights have been adjusted to accommodate the new variable, and to reflect concern by non-minority as well minority students. (Minority students place a greater weight on diversity.) A new definition to extend the student and faculty diversity variables to "Overall satisfaction" in other student levels also has been provided.

1.5 Scholarship, broadly defined has been added under "Miscellaneous functions." Used in the Trustee evaluation score, this new variable depends on: the average over regular faculty sims of scholarship performance and research performance; the average over all faculty sims of educational development time; and technology utilization in teaching.

2. Investment Return
1. Endowment Total Return

Sections 5.2 and 5.3 of my 30 August notes are amended to read as follows. The changes provide final parameter values and clarify the formulas.

• [5.2 in the 30 Aug. Notes] The parameters (revised from this note’s original draft) are provided on the new HE.RespF_Definitions:Investments spreadsheet and shown below. The expected values have the dimension "percent change per year" net of inflation.



• [5.3 in the 30 Aug. Notes] The mean and standard deviation for the endowment’s real monthly total return depend on the asset allocation and, following the dividend discount model for investment returns, the change in the inflation rate. Nominal total return equals inflation plus real return. Let f_i be the fraction of the endowment invested in category i. Then:

endowment monthly growthrate =

changeInMonthlyInflationRate +
where w_i is the fraction of the portfolio invested in asset class i
and m_i is the annual expected real return for asset class i.

endowment annual standard deviation =
where the s_ij are the entries in the covariance table.

The formulas for the annual real return and standard deviation are
included in HE.RespF_Definitions:Investments. Applying them
with an asset mix of 50% large-cap stocks, 20% small-cap stocks,
and 30% bonds produces an expected real return of 5.7% and a
portfolio standard deviation of 18.6%.

endowment monthly standard deviation =
Sqrt[endowment annual standard deviation –
12(standard deviation of monthly inflation)²/(1–lambda)]/Sqrt[12]
where lambda is the latency factor for the change in monthly inflation.

• [5.4 in the 30 Aug. Notes] Endowment[month t] = Endowment[month t–1] *
(1 + random normal deviate with the above mean and standard deviation +
any growth or decline due to scenario or chance-card events)

2. S&P 500 Total Return

The total return from the S&P 500 stock index is displayed as a benchmark in the Investment Management Office. It should be calculated as follows:



where endRandV is the random normal deviate used in the preceding equation for endowment and SapRandV is a new random normal deviate with:

mean = changeInMonthlyInflationRate + expected real return for large-cap stock (6%) minus expected real return of the endowment

standard deviation = standard deviation for large-cap stocks (22%) and the standard deviation of the endowment

3. Equilibrium Endowment Payout Rate

My writings on college and university finance stress the importance of long run financial equilibrium. CyberCampus would be less than complete if it fails to include this important concept, yet until now a practical method for doing so has eluded me. Further thinking about the Investment Office interface and how to simplify the trustee evaluation score has triggered a breakthrough. The equilibrium payout rate should be displayed on the Investment Office screen backed up with the following explanatory note, and I have incorporated it in the revised trustee evaluation scoring formula.

Explanatory note: The equilibrium endowment payout rate is the fraction of the endowment’s beginning market value that can be spent each year without depleting the its value relative to budget needs. The equilibrium calculation takes account of the school’s investment asset allocation, expenditure growth policies, and the growth of tuition and other current revenue. Institutions that limit endowment spending to the equilibrium payout stand the best chance of being able to sustain their policies over a multi-year planning horizon.

The equilibrium payout rate is calculated as follows. Let:

p = the equilibrium payout rate

r = expected real annual return on the endowment portfolio based on Player’s current asset allocation

r = real increase in total expenditures (including transfer to plant and debt service) as determined by the immediately previous Stage-1 resource allocation run. Calculate the overall growthrate of total expenditures and then subtract the inflation rate used in doing the Stage-1 calculation.

i = real increase in non-endowment income as determined by the last Stage-1 resource allocation to be run. Calculate the overall growthrate of total income from all sources other than endowment and then subtract the inflation rate used in doing the Stage-1 calculation.

g = the smoothed value of gifts to endowment for the prior year divided by the endowment market value at the beginning of the year. Set lambda equal to 0.6. For initialization, take the ratio of initial gifts to endowment to endowment market value.

E = market value of the endowment the last time the Stage-1 resource allocation was run

B = dollar value of total expenditures after the last Stage-1 resource allocation

I = dollar value of total non-endowment income after the last Stage-1 resource allocation

The equilibrium payout rate is obtained by solving the following quadratic equation:



This is solved by taking the positive root in the quadratic formula. We guard against imaginary and other unacceptable solutions by setting a lower bound on the payout rate: tentatively 0.04, based on institutional experience. Values lower than this generally prove unsustaintable from the point of view of campus politics and donor reaction to fund-raising efforts. Hence the calculating formula becomes:



4. Course Type Determination

Section 6.8 of my Note of 30 August states: "The course mix preferences for conventional courses (seminar, general, lecture with breakout) will be a Player input. The Course_Templates sheet in HE.GDB.init and the reference to it on the Dept_Master sheet have been eliminated. The maximum class size for DL courses has been added as column E of Dept_Master." This is now AMENDED to read as follows.

• [6.8 in the 30 Aug. Notes] The maximum class size for DL courses has been added as column E of Dept_Master.

• [6.9 in the 30 Aug. Notes] Players will input their course mix preferences for conventional courses (seminar, general, lecture with breakout). Departmental faculty have their own intrinsic preferences for course type mix (and also for normal class size). These will be supplied on HE.GDB.init:Course_Templates. The departmental course preference used each trimester (t) will be calculated as follows:



where x_it^P is the player’s preference for course type i as of time t, x_i^D is the department’s intrinsic preference (which doesn’t vary over time), and l=0.6.

5. Factors That Vary Over time

Factors such as inflation, interest rates, exogenous growthrates, student preferences for majors, and peer-institution should change over time. All factors will be subject to random variation according to a so-called autoregressive scheme that includes the possibility of serial correlation.

1. General Scheme

The general scheme is defined below. The list of applicable variables and the parameter values for each variable are provided in a new spreadsheet: HE.RespF_Definitions:Time_Variation. This procedure replaces Section 8.3 of my note of 30 August.

Let x_t be the value of a particular variable at time t. The variable might be the monthly inflation rate, for example, in which case t would represent months. The general formula for computing x_t is:



where e_t is a random normal deviate, and b₁ and b₂ are parameters. The mean of the random variable is always zero. The two b-parameters and the "base" standard deviation for each variable are provided in the Time_Variation" spreadsheet. The initialization values, x[t–1] and x[t–2], should be set to zero in all cases. (The three parameters on the right are for my reference and can be ignored.)

If we wish to vary the standard deviation for some variables according to the degree of difficulty of the game, I suggest we multiply the indicated standard deviations by:

0.5 for "easy" games,
1.0 for "medium" games, and
1.5 for "hard" games.

Values for intermediate settings, if any, can be set proportionally. (As always, because it’s hard to predict the exact results of these settings, we may want to adjust the multipliers during beta.)

Explanatory comment. Depending on the parameter values, the autoregressive scheme can superimpose a degree of periodicity on the random series. Setting b₁ = +0.538 and b₂ = –0.758, for example, produces a tendency toward oscillation with a natural frequency of 5 periods and a damping factor of 0.5 (i.e., the series decays to half its value in one cycle). Setting b₁ = +1.681 and b₂ = –0.942 produces a tendency toward oscillation with a natural frequency of 12 periods and a damping factor of 0.7. The system doesn’t follow these patterns exactly because each period it is displaced by a new random shock. Setting the standard deviation to an appropriate level insures that an appropriate level of oscillatory behavior comes through in the actual random series. Setting b₂ = 0 eliminates the oscillations and produces simple monotonic latency instead.

2. Monthly and Annualized Values

Some variables change each month, some on longer cycles. Inflation changes on a monthly basis, yet conversion of certain financial variables from real to nominal terms requires an annual inflation rate. For example, real growth of other operating income is specified in annual terms, but the value actually used in calculations requires addition of the annual inflation rate. Section 8 of WFM Notes of 30 August discusses the so-called "monthly change in the inflation rate," which mostly I have simply called "inflation." Section 8.5 defines the annualized inflation rate as being the average of the inflation rates (a.k.a., changes in inflation) during the last twelve months. This definition is hereby AMENDED to be the SUM of the inflation rates during the last twelve months. In the example above, the nominal growth, for the year, of other operating income equals the real growthrate plus the annualized inflation rate.

3. Interest Rates

Section 8.6 of the Note of 30 August is hereby AMENDED so that the short-term real interest rate for positive operating reserves ("Bank rate") is subject to random variation. The figure given there (0.5%) should be used as the initialization value. The borrowing rate will always be 4 percentage points greater than the bank rate. The long-term nominal interest rate on facilities and student residence borrowing also will be subject to random variation. The initialization value should be set to 6.75% plus a random normal deviate with mean zero and a standard deviation of 0.25%.

The spreadsheet provides the time-series randomization parameters for short- and long-term interest rates. The resulting random values are used as follows:

Consistent with real-world financial markets, the long-term rate depends on the change in the inflation rate as well as the current random factor. (Note that this is a nominal, not real, rate.) Both rates are subject to floors to prevent nonsensical values.

4. Peer-Institution Faculty Salaries

Faculty salaries by rank are calculated for each peer institution. We agreed in Hong Kong that the comparison set to be displayed will be a one-in-n sample of the whole dataset. My recollection is that we are not going to display the salaries by rank for all the comparison institutions. Therefore, there is no need to make the salaries for individual institutions vary over time. I suggest that, at initialization, we calculate the average salaries over (say) the 3 closest institutions (in terms of prestige) above and below the PGI, make these vary over time using the parameters in the spreadsheet, and use the result as "peer-institution salaries in the faculty satisfaction index and any reporting.

The salary change for a given rank equals the sum of:

salaryGrowthrate = annualizedInflation + generalRandFactor + specificRandFactor,

where the parameters for the two random factors are specified on the spreadsheet. The new salary equals the prior-year’s salary plus times (1+salaryGrowthrate ). To move from the rank category for full professors to the age-rank category for full professors: (a) assume the calculated full-professor figure applies to the middle age-rank category, then (b) use the ratios for the prior to get the other two age-rank categories. Set the initialization ratios to the ratios used in initializing the PGI full professor salaries.

5. Student preferences for major

Students’ preferences change over time, and players may need to adjust their strategies to take this into account. Parameters for the requisite random variation are contained on the spreadsheet. The resulting random variables should be used as follows:

where i and j refer to fields and e_i is the newly-drawn random variable for field i. Students should reassess their preferences annually. The adjustment should be made for all fields, in case the Player decides to introduce a new field at some future time. As noted elsewhere, the actual preferences used in field selection are normalized so that the figures sum to one for the fields currently included in the game.

6. Average Time to Degree

In Hong Kong we noted the problem of initializing the time-to-degree statistics. We considered eliminating time to degree from the interface reports, but on reflection I have concluded this is not a good idea. Time to degree represents an important dimension of institutional performance, one that Jesse and I are particularly interested in. Dropout rates are also important and should be included.

The time-to-degree and dropout figures should probably be displayed as time series in the student union. There is one pair of figures for each student level.

The initialization values can be found on the revised "HE.GDB.init:Student_Pars".

• Time to degree
  SL-1 cell AG14
  SL-2: cell AG15
  SL-3: cell AG56
  SL-4: cell A102
  SL-5: displace the SL-2 figure by a random normal deviate with mean
  zero and standard deviation = 0.25 years (so they aren’t
  the same)
• Dropout rate
  SL-1 cell B15
  SL-2: cell B19
  SL-3: cell B57
  SL-4: cell C99
  SL-5: displace the SL-2 figure by a random normal deviate with mean
  zero and standard deviation = 0.025 (so they aren’t
  the same)

Going-year values are calculated as follows:

• Time to degree: average the number of years in program for the students who graduate in a given year.
• Dropout rate: number of students dropping out in a given year divided by an exponential moving average of the size of the entering class. The moving average used in the denominator is:
  aveEntClass[t] =
  (1-lam)*(size of entering class this year) + lam*aveEntClass[t–1]

1. Trustee Evaluation Score

We agreed in Hong Kong that the trustee evaluation score should be simplified and that I should provide brief descriptions of what the player can do to affect each score component. The RespF_Defnitions:Trustee_Eval.rev spreadsheet provides the new, simplified variable definitions and weights. The number of general performance indicators has been reduced from 26 to 11, and the number of financial indicators from 7 to 4. The remaining general indicators have been reorganized from the original five categories into three categories: outputs, institutional performance indicators, and attitudes toward the institution.

The general performance variables contribute positively to the trustee evaluation. The financial indicators contribute positively at a declining marginal rate if they are better than a prespecified benchmark level, as indicated in the formula below. Poor financial performance relative to the benchmark deducts trustee evaluation points at an increasing marginal rate. This formulation allows finances to exert modest effects as long as the institution’s financial situation is healthy. However, poor financial performance can erase other good outcomes and, if bad enough, come to dominate the equation. This conforms to reality and teaches an important lesson.

1. Changes in variable definitions

The variables have the same definitions as previously except as follows.

• The definition of Degrees granted has been elaborated to better reflect the influence of the various student levels. We begin by defining the ratio of degrees granted during the last year (D_it) to degrees granted at initialization (D_i0), where i refers to student level, according to:

• Sponsored research activity depends on the ratio of the current level of research activity, obtained by adding up the total direct volume of active research projects for all faculty sims, to the initialization value. Unlike the case of degrees, we must guard against situations where the initialization value or the current value equals zero. We do this by defining:

• The financial variables follow the following general form:

1. Descriptions of the variables

The requested brief descriptions of the scores and what the player can do to affect them follow.

• Degrees granted: a widely-used measure of educational output. Players can increase degree production either by increasing student intake or by improving the graduation rate. Intake can be affected by increasing the matriculations target for existing student levels or by starting programs for levels not currently served—provided there are sufficient numbers of qualified applicants. The graduation rate can be increased by reducing course denials and failures: that is, by adjusting faculty numbers and incentives to improve course availability and teaching quality, and by improving student qualifications and satisfaction.
• Sponsored research activity: a readily-measured surrogate for research output. Sponsored research reflects success in the competition for funding, which in many fields is closely correlated with the quantity and quality of research . Players can influence sponsored research by adjusting faculty incentives to favor research and scholarship, by hiring faculty with greater research talent, by adjusting faculty salary policy to improve researcher retention and satisfaction, and by cutting the research overhead rate to give more of the research dollar to principal investigators.

• Institutional prestige: a widely-used though subjective and controversial surrogate for institutional quality. Players can increase prestige by improving the academic standing of departments, which in turn depends on faculty research performance, sponsored research funding, and the existence and quality of doctoral programs. Prestige also depends on the applications ratio and yield rate for traditional undergraduates—which can be affected by varying admissions, financial aid, and tuition policies—and on the level of athletic competition and win-loss record which can be affected by direct player decision, by spending on athletics, and by admissions and financial aid policies for athletes.
• Educational quality: the so-called "value added" of the institution’s educational programs which would be listed as an output but for the difficulties of measurement. Players can influence educational quality by adjusting incentives to favor educationally-related functions, by hiring faculty with greater teaching talent, by adjusting faculty salary policy to improve teacher retention and satisfaction, and by adjusting student-faculty ratios and course type mix. Scholarship and research enhance educational quality if they can be achieved without undermining the focus on educational tasks. Investments in libraries and technology utilization in teaching also will improve educational quality.
• Scholarship, broadly defined: reflects Earnest Boyer’s Scholarship Reconsidered, which includes the scholarship of integration, of application, and of teaching as well as knowledge creation. Players can boost their score by improving faculty scholarship and research performance, faculty time spent on educational development and public service, and technology utilization in teaching.
• Student diversity: the percentage of students who are minority. Players can increase student diversity by adjusting admissions and financial aid policies.
• Faculty diversity: weighted average percent faculty who are minority (70% weight) and percent who are women (30%). Players can increase faculty diversity by adjusting hiring policies.
• Percent alumni who have given during the last five years: a surrogate for the effectiveness of fund-raising efforts and alumni satisfaction. Players can improve this statistic by increasing spending on institutional advancement, and the school’s prestige, educational quality, financial performance, and athletics record.

• Faculty morale: important for long-term institutional well-being. Players can boost faculty morale by increasing salaries, decreasing teaching load, aligning incentives with the faculty talent mix, providing infrastructure to increase performance, increasing faculty and student diversity, and refraining from policies that conflict with faculty preferences for time utilization and summer teaching.
• Student morale: important for student achievement, applications and yield, and retention. Players can improve student morale by increasing educational quality, boosting spending on libraries and student life, adjusting faculty numbers and course mix to reduce course denials, and boosting the use of IT in teaching.
• Staff morale: important for administrative and facilities management productivity. Players can influence staff morale mainly by adjusting staff salary policy. Facilities staff also lose morale if O&M funding falls short of the level needed to maintain the plant.

• Current surplus (deficit) as a percent of operating revenues: the degree to which the current budget augments or erodes the institution’s financial viability. Player determine the current surplus or deficit by adjusting overall financial policies.
• Smoothed surplus (deficit) as a percent of operating revenues: the degree to which the budget trends augment or erode the institution’s financial viability. Player determines the current surplus or deficit by adjusting overall financial policies as decided over a period of years.
• Endowment payout rate (relative to the equilibrium payout rate): for endowed institutions, indicates whether current financial policies will turn out to be viable over time. Players can determine the payout rate by adjusting overall financial policies.

1. Penalty Score

Section 11 of WFM Note of 9 September contains a formula for "multiplierForPromises." The formula contains an error. The note has been corrected as follows: