Enrollment Growth and Faculty Hiring at Public Research Universities

Declines in state appropriations have decreased the ability of public research universities to hire faculty, particularly tenure line faculty. Many universities have grown nonresident enrollment as a substitute for state funding. This study investigates whether faculty hiring was associated differently with nonresident enrollment growth versus resident enrollment growth. Grounded in labor demand theory, to study this relationship we estimate institution-level panel statistical models for the academic years 2002–2003 to 2016–2017. Results indicate that nonresident enrollment growth had a stronger positive association with full-time tenure line hires than resident enrollment growth. In contrast, employment of full-time and part-time non-tenure track faculty was not associated differently to nonresident versus resident enrollment growth. The institutional policy implication is that nonresident enrollment growth may be a viable strategy to finance tenure line faculty hires. However, state policymakers should recognize that many public research universities and most regional public universities face weak nonresident enrollment demand and are unlikely to compensate for declines in state funding by growing nonresident enrollment.

Keywords: Nonresident enrollment; Tenure-line faculty; Non-tenure track faculty; Labor demand

Cuts to state higher education funding raise concerns that, on one hand, public universities no longer have the resources necessary to educate students (Bound & Turner, [13]; Kane & Orszag, [44]) and, on the other hand, public universities increasingly value revenue generation and prestige over the historical mission of social mobility for state residents (Gerald & Haycock, [34]; Slaughter & Rhoades, [63]). At public research universities, average state appropriations declined from about $253 million in 2002–2003 to $198 million in 2013–2013, as shown in the top panel of Fig. 1 (Author calculations, 2018 CPI). Despite a prolonged period of economic recovery, state appropriations only rebounded modestly to $216 million by 2016–2017.

Graph: Fig. 1 Revenue and faculty employment, 2002–2003 to 2016–2017. Prior to 2013, faculty were defined as those whose primary occupation included instruction and/or research and/or public service. After 2013, faculty were defined as all individuals whose primary occupation includes instruction

Public research universities have responded to state funding cuts by changing both spending behavior and revenue generating behavior. On the spending side, faculty are the largest single labor cost by research universities (Commonfund Institute, [21]; Ehrenberg, [26]). Furthermore, higher education institutions expend a greater share of resources on personnel than any other industry, as higher education is relatively labor-intensive and employs a large share of highly educated workers (Archibald & Feldman, [4], [5]). Scholars warned that state cuts force public research universities to hire fewer tenure line faculty and to increase student-to-faculty ratios (Kane & Orszag, [44]; Kane et al., [45]). State cuts also cause universities to shift from tenure line faculty to less expensive non-tenure track (NTT) substitutes (Ehrenberg, [27], [28]; Frye, [32]). The bottom panel of Fig. 1 shows that from 2002–2003 to 2016–2017, the mean number of full-time NTT faculty at public research universities increased 42% from 493 to 854 and the number of part-time NTT faculty increased 30% from 467 to 606, while the number of tenure line faculty increased only 8% from 932 to 1005 (Author calculations).

On the revenue side, public research universities respond to state cuts by seeking alternative funding sources. Scholarship often highlights efforts to grow revenue from research (e.g., Slaughter & Leslie, [62]; Slaughter & Rhoades, [63]) and from donations and investment (e.g., Cheslock & Gianneschi, [18]). However, tuition revenue is the largest revenue source for most public research universities. The top panel of Fig. 1 shows that average net tuition revenue increased from $162 million in 2002–2003 to $344 million in 2016–2017. Nonresident students, who face two- to three-times larger tuition prices (College Board, [20]), have become an important source of tuition revenue for universities as state appropriations have stagnated (Jaquette & Curs, [41]). From 2003–2004 to 2016–2017, the mean number of full-time freshmen at public research institutions paying nonresident tuition increased 74% (from 622 to 1084) while the mean number of freshmen paying resident tuition increased 15% (from 2671 to 3075).

Nonresident enrollment at public universities has become a controversial policy issue, with several states adopting or proposing nonresident enrollment caps (e.g., California State Legislature, [8]). Normatively, critics argue that state flagship universities should focus on educating state residents (e.g., Haycock et al., [36]). Empirically, nonresident enrollment growth has been associated with some undesirable outcomes, such as declines in the percentage of Pell recipients and the percentage of students who identify as Black or Latinx, thereby contributing to socioeconomic and racial isolation on campus (Jaquette et al. ([42]). Contrary to claims by university administrators that nonresident enrollment enables public universities to finance resident access, Curs and Jaquette ([24]) found that nonresident enrollment growth had no effect on resident enrollment at most public research universities and negatively affected resident enrollment at prestigious public research universities.

Researchers have not examined the effect of nonresident growth on faculty hiring. Although prior research examines general relationships between enrollment and faculty employment (e.g., Zhang et al., [68]; Zhang & Liu, [69]), nonresident students pay higher prices than residents, raising the possibility that nonresident enrollment growth enables universities to hire more faculty or to hire tenure line as opposed to NTT faculty. However, depending on their preferences, universities may not expend nonresident tuition revenue on faculty hiring. This paper attempts to answer two research questions. What is the association of resident freshmen enrollment with faculty hiring? What is the association of nonresident freshmen enrollment with faculty hiring? Addressing these research questions can inform institution-level and state-level policy decisions about nonresident enrollment.

To answer these research questions, we model three dependent variables: tenure line faculty hires, full-time NTT faculty hires, and part-time NTT faculty employment. We analyze the population of 136 public research universities from 2002–2003 to 2016–2017, utilizing a fixed effects estimation strategy and including institution-varying, time-varying covariates motivated by labor demand theory.

This study is practically significant because faculty, particularly tenure line faculty, are essential to the research mission (Ehrenberg, [26]; Kane & Orszag, [44]) and governance (Legon et al., [49]; Rhoades, [59]) of public research universities. Furthermore, most studies find that being taught by part-time NTT faculty negatively affects student outcomes (e.g., graduation, retention, academic standards, interactions with students) (Bettinger & Long, [11]; Ehrenberg & Zhang, [30]; Jaeger & Eagan, [39]; Umbach, [64]; Baldwin & Wawrzynski, [9]; Johnson, [43]), though some studies find positive effects (e.g., Bettinger & Long, [12]; Figlio et al., [31]). Nevertheless, research unequivocally finds that higher student-faculty ratios and larger class sizes negatively affect student outcomes (e.g., Arias & Walker, [6]; Beattie & Thiele, [10]; Garcia-Estevez & Duch-Brown, [33]; Mandel & Sussmuth, [52]). Given the importance of faculty to universities and the long-term decline in state funding, it is important for universities to identify alternative means of faculty hiring.

This section introduces core concepts from labor demand theory, applies these concepts to identify mechanisms linking enrollment growth to faculty hiring, and finally situates our research vis-à-vis previous empirical research on the determinants of faculty employment.

Labor demand theory builds on the theory of the firm, which assumes that the goal of firms is to maximize profit, defined as $PQ-c\left(L,K\right)$ , where revenue is the product of price ( $P$ ) and quantity ( $Q$ ) and costs ( $c$ ) are a function of labor ( $L$ ) and capital ( $K$ ). This maximization equation must be modified to model the behavior of public research universities, which cannot distribute profits (Bound & Turner, [13]). Rather than making strong a priori assumptions about university mission (e.g., human capital creation, prestige), we assume that public research universities attempt to maximize utility subject to a non-distribution constraint, and that they produce two primary products: education and research.[1]

We construct a simple revenue and cost equation for public research universities. Universities sell enrollment ( $e$ ) at price $P_e$ (e.g., tuition price) and quantity $Q_e$ . They also sell research ( $r$ ) at price $P_r$ (e.g., the funding associated with a research grant) and quantity $Q_r$ . Thus, operating revenues consist of tuition revenue—defined as $P_e{Q}_e$ – and research revenue—defined as $P_r{Q}_r$ . In addition to operating revenue, universities receive subsidy revenue ( $S$ ), comprised of state appropriations, endowment income, and donations (Bound & Turner, [13]; Winston, [66]). These revenues from tuition, research, and subsidy are expended to pay for the costs of Labor $L$ (e.g., faculty, administrators) and capital $K$ (e.g., classrooms, dormitories, equipment) (Bound & Turner, [13]). Given the non-distribution constraint, the relationship between revenues and costs can be described as:

Graph

Equation (1) motivates a general labor demand function for faculty of a particular contract type ( $c$ ) (e.g., tenure line faculty, full-time NTT faculty, part-time NTT faculty) employed by a university:

2 $$L_c\left(w_c\right)=f\left(w_c,w_c^{\prime },k,P_e,Q_e,P_r,Q_r,S\right)$$

Graph

where $w_c$ is the market wage of faculty labor with contract type $c$ and $w_c^{\prime }$ is the market wage of substitute faculty labor (i.e., not of type $c$ ). For example, if contract type $c$ is tenure line faculty, then $w_c^{\prime }$ refers to the wage of full-time NTT faculty and part-time NTT faculty. $k$ is the rental rate of capital. $P_e,Q_e,P_r,Q_r,S$ are revenue components, described previously. Equation (2) highlights that universities have separate labor demand functions for each faculty contract type $c$ . Therefore, demand for a particular faculty contract type is a function of the relative costs of that contract type ( $w_c,w_c^{\prime },k$ ), revenues ( $P_e,Q_e,P_r,Q_r,S$ ), and preferences.

Faculty costs differ by contract type (Anderson, [3]; Cross & Goldenberg, [23]; Ehrenberg & Klaff, [29]). Tenure line faculty cost the most in terms of salary and benefits and reduces budget flexibility in that they cannot be laid-off to cut costs due to budgetary needs. Full-time NTT faculty often hold multi-year but not life-long contracts. They typically have lower costs per credit hour than tenure line faculty because they receive lower salaries, lower benefits, and teach higher course loads. Part-time NTT faculty are paid less than full-time NTT faculty, typically do not receive benefits, and increase budget flexibility because they are often hired on a per-course basis.

The labor demand curve $L_c\left(w_c\right)$ for a particular faculty contract type $c$ is downward sloping, meaning that the quantity demanded decreases (i.e., a movement along the demand curve) as the price of labor $w_c$ increases. The prices of substitute labor $w_c^{\prime }$ are demand shifters. For example, the labor demand curve for tenure line faculty shifts leftward if the market wage for full-time NTT faculty or part-time NTT faculty declines.

Universities differ in the amount of utility they derive from a particular faculty contract type because preferences differ across universities. For example, a university that values both research and teaching may place relatively higher value on tenure line faculty. A university that values teaching more than research may place relatively higher value on full-time NTT faculty.

Finally, the components of revenues— $P_e,Q_e,P_r,Q_r,S$ —are also demand shifters for $L_c$ . Revenues constrain how many faculty of each contract type a university can afford to hire. Considering the three broad revenue streams of tuition ( $P_e{Q}_e$ ), research ( $P_r{Q}_r$ ), and subsidy ( $S$ ), a decline in one revenue stream may compel universities to shift from tenure line faculty to less expensive substitutes.

The labor demand model described above posits that the quantity of labor is a function of the revenue associated with the output created by that labor. In perfectly competitive markets, it is assumed that the price and quantity associated with each output are determined within the market and outside of the firm's direct control. Thus, the implications of the labor demand model would imply that institutions hire faculty to produce an optimally determined level of output.

However, public higher education institutions are not operating within perfectly competitive markets; thus, the prices and quantities of their outputs are at least partially determined through active choice (Weisbrod et al., [65]; Winston, [66]). Within the context of our study, it is likely that higher education institutions are likely jointly making the decision to hire more faculty alongside the decision to grow and/or change the mix of enrollments (Cheslock & Kroc, [19]) or grow revenues associated with research (Cheslock & Gianeschi, [18]). The joint nature of these decisions within the higher education context blurs the direct causal mechanism posited within the labor demand framework.

We apply labor demand theory to the relationship between enrollment growth and faculty hiring. To begin, we compare an increase in subsidy revenue to an equivalent increase in tuition revenue due to enrollment growth. Consider a donation of $1 million per year for 4 years, with no restrictions except that the gift cannot be added to the permanent endowment. Alternatively, consider freshmen enrollment growth of 100 students, who each pay $10,000 in annual tuition, yielding tuition revenue of $1 million per year ( $P_e{Q}_e=10,000\ast 100=1,000,000)$ for 4 years. With respect to Eq. (1) linking university revenues and costs, the donation revenue increases subsidy ( $S$ ) by $1 million per year for 4 years but does not directly affect costs. Therefore, the university has discretion to allocate the donation revenue across labor and capital costs.

Enrolling 100 additional students also increases operating revenues by $1 million per year for 4 years. However, enrollment growth directly increases costs because enrolling additional students requires expenditure on capital and labor. If the university cares about maintaining some level of quality of education that each student receives, then enrolling 100 additional students will cause the university to hire additional faculty to teach these students (Bound & Turner, [13]). This mechanism suggests a strong, positive relationship between enrollment growth and faculty employment.

Next, compare enrolling an additional 100 nonresident freshmen to an additional 100 resident freshmen. Marginal tuition revenue is higher for nonresident students, since a full-time nonresident freshman at a public research university generates about $20,700 in net tuition revenue compared to about $6600 on average per resident freshman (Jaquette et al., [42]). Assuming these values, enrolling 100 additional nonresident freshmen is expected to increase net tuition revenue by $2,070,000 compared to $660,000 per year for 100 additional resident freshmen. These figures suggest that nonresident enrollment shifts out the budget constraint more than resident enrollment growth, enabling universities to hire more faculty or to hire tenure line faculty rather than less expensive NTT faculty. By contrast, the lower marginal revenue from resident tuition may compel universities to hire NTT faculty in response to resident enrollment growth.

Although revenues constrain the number and type of faculty universities can afford to hire, the combination of revenues and university preferences dictate the number and type of faculty hired. For example, universities that prioritize access for low-income students may allocate the majority of nonresident tuition revenue towards need-based institutional aid rather than faculty hiring. By contrast, universities that prioritize student academic profile may expend more on institutional merit aid. Moving beyond labor demand theory, which assumes that preferences are independent of revenues, most sociological theories of organizational behavior—e.g., resource dependence theory (Pfeffer & Salancik, [58]) and academic capitalism (Slaughter & Leslie, [62])—assert that organizational preferences are influenced by the preferences of important resource providers. Nonresident students tend to be more affluent than residents (Jaquette et al., [42]). To the extent that affluent nonresident students value consumption amenities (Armstrong & Hamilton, [7]; Cooke & Boyle, [22]; Mixon & Hsing, [53]) (e.g., luxury facilities and big-time college athletics), a university may allocate nonresident tuition revenue towards these nonacademic expenditures (Jacob et al., [38]).

We situate our research within the literature on determinants of faculty employment.

These studies typically model the number or proportion of faculty of a particular contract type (e.g., number of tenure line faculty or proportion of faculty who are tenure line) as a function of the labor demand determinants identified in Eq. (2).

Consistent with the notion of a downward sloping labor demand curve, studies found that faculty salary has a strong, negative relationship with the number of faculty of that contract type employed by the university (e.g., Cheslock & Callie, [17]; Ehrenberg & Klaff, [29]; Liu & Zhang, [50], [51]; Zhang & Liu, [69]; Zhang et al., [68]). These studies also tend to support, albeit less strongly, the idea that employment levels for a particular faculty contract type are sensitive to the price of substitute faculty contract types.

A central concern of the faculty employment literature has been explaining the shift from tenure line to NTT faculty. Scholars argue that this shift was made possible by growth in the production of PhDs, which caused the supply of PhD-educated labor to increase and their market wage to decline. Thus, universities that faced a growing supply of cheap faculty labor increasingly hired NTT faculty rather than tenure line faculty (e.g., Anderson, [3]; Ehrenberg, [28]; Roemer & Schnitz, [60]). Consistent with this idea, Liu and Zhang ([50], [51]) found that universities located in metropolitan areas employ a greater share of part-time NTT faculty because metropolitan areas have a large supply of potential part-time faculty.

Revenues constrain the number and type of faculty universities can afford to hire. At the broadest level, research finds that total institutional revenues per student is positively related to the number of tenure line faculty (Ehrenberg & Klaff, [29]; Zhang & Liu, [69]; Zhang et al., [68]) and negatively related to the number of part-time faculty (Liu & Zhang, [51]; Zhang et al., [68]).

Historically, state appropriations were the largest source of subsidy revenue for public universities. Frye ([32]) found that state appropriations per FTE student had a positive relationship with the number of tenure line faculty, the number of full-time NTT faculty, and a negative relationship with part-time NTT faculty. Similarly, Cheslock and Callie ([17]) found that business schools responded to state cuts by decreasing the number of full professors and increasing the number of assistant professors. Brown et al. ([14]) found that negative shocks to endowment caused research universities to decrease tenure line faculty employment. Collectively, these studies suggest that subsidy revenues from state appropriations and endowment influence whether universities hire more expensive faculty types.

Few studies analyze tuition revenue or enrollment levels as determinants of faculty employment. Cross-sectional analyses by Liu and Zhang ([67], [51]) found that tuition reliance was associated with growth in the proportion of part-time NTT faculty at 4-year universities. Dynamic panel models by Zhang et al. ([68]) found that growth in the number of FTE students was positively associated with growth in the number of tenure line faculty and full-time NTT faculty at research universities, but not the number of part-time NTT faculty.

We argue that scholarship on faculty employment requires more nuanced analyses of enrollment growth because state appropriations have declined and tuition revenue is now the largest revenue source at most public universities. Many public universities responded to declines in state appropriations in the 2000s by growing nonresident enrollment (Jaquette & Curs, [41]). Consistent with the finding from Zhang ([67]) that research universities enjoy relatively higher demand from nonresident students, nonresident enrollment growth was stronger at research universities than regional universities. Compared to residents, nonresident students pay higher prices and, thus, shift out the budget constraint more. However, prior research has not compared how the relationship between enrollment and faculty employment varies for resident versus nonresident enrollment growth.

The labor demand function $L_c\left(w_c\right)=f\left(w_c,w_c^{\prime },k,P_e,Q_e,P_r,Q_r,S\right)$ from Eq. (2) states that university demand for a particular faculty contract type $c$ is a function of wages ( $w_c$ ), wages of substitute faculty ( $w_c^{\prime }$ ), rental rate of capital ( $k$ ), the price ( $P_e$ ) and quantity ( $Q_e$ ) of enrollment, the price ( $P_r$ ) and quantity ( $Q_r$ ) of research, and subsidy revenues ( $S$ ). Equation (3) represents our empirical framework, a reduced form labor demand function written as a linear institution-level panel model:

3 $$Y_{\mathit{it}}=X_{\mathit{it}}\beta +W_{\mathit{it}}\theta +{\delta }_t+{\alpha }_i+{\epsilon }_{\mathit{it}}$$

Graph

where subscript $i$ represents institutions and subscript $t$ represents time, in years. $Y_{\mathit{it}}$ represents alternative faculty employment dependent variables.

We modeled three dependent variables: (1) the annual number of tenure line faculty hired; (2) the annual number of full-time NTT faculty hired; and, (3) the annual total employment of part-time NTT faculty. $X_{\mathit{it}}$ represents the independent variables of interest, comprising of a matrix of $k$ measures of freshmen enrollment at institution $i$ in time $t$ . We estimated models where $k=1$ and $X_{\mathit{it}}$ was a single measure of total freshmen enrollment. We also estimated models where $k=2$ and $X_{\mathit{it}}$ consisted of a measure of resident freshmen enrollment and a measure of nonresident freshmen enrollment. The coefficients of interest are represented by $\beta$ , a vector of length $k$ that represents the relationship between freshmen enrollment measures and the faculty employment outcome. $W_{\mathit{it}}$ is a matrix of unit-varying and time-varying covariates. ${\delta }_t$ represents a year-varying, institution-invariant component. ${\alpha }_i$ represents institution-varying, time-invariant component. Finally, ${\epsilon }_{\mathit{it}}$ , represents an institution-varying, time-varying error term.

We hypothesized that the timing of the relationship between freshmen enrollment growth and faculty hires was likely to be time-lagged. As an example, consider the relationship between Fall 2014 freshmen enrollment and tenure line faculty hires. If universities respond quickly to information (e.g., enrollment deposits) regarding projected growth in Fall 2014 enrollment, tenure line faculty positions are approved in Spring/Summer 2014, faculty search occurs during the 2014–2015 academic year, and the employment contract for new hires begins Fall 2015 of the 2015–2016 academic year. This timing would suggest a 1-year time lag between enrollment growth and tenure line hires. However, if universities wait until Fall 2014 freshmen are enrolled before approving new requests, then faculty search occurs during the following academic year (2015–2016) and new hires begin in Fall 2016 of the 2016–2017 academic year, suggesting a 2-year lag between enrollment growth and tenure line hires. Alternatively, if the relationship between enrollment and faculty hiring is anticipatory rather than reactive, a zero-year lag between enrollment growth and tenure line hires may be plausible. Compared to tenure line hires, time lags may be shorter for full-time NTT hires, which typically require a less restrictive approval process (Ehrenberg, [26]), and shorter still for part-time lecturers who are often hired on a just-in-time basis (Kezar & Gehrke, [47]).

The relationship between freshmen enrollment and faculty hires may occur over several time periods rather than a single time period. Additionally, the timing of this relationship likely differs across universities and across academic units within universities. Distributed-lag models estimate the cumulative or long-term relationships in contexts where the relationship between regressors and an outcome occurs over several time periods and when the timing of the relationship differs across units (Almon, [2]; Dell et al., [25]; Jaquette, [40]). Equation (4) modifies the fixed effects panel model from Eq. (3) to include current and lagged values of freshmen enrollment measures, $X_{\mathit{it}}$ :

4 $$Y_{\mathit{it}}=\sum _{j=0}^L\left(X_{i,t-j}{\beta }_j\right)+W_{\mathit{it}}\theta +{\delta }_t+{\alpha }_i+{\epsilon }_{\mathit{it}}$$

Graph

where $j$ represents the jth lag on freshmen enrollment (e.g., $j=0$ refers to current freshmen enrollment, $X_{\mathit{it}}$ , and $j=1$ refers to freshmen enrollment last year, $X_{i,t-1}$ ); $L$ represents the total number of lagged values of freshmen enrollment in the model (if $L=0$ then only current freshmen enrollment, $X_{\mathit{it}}$ , is included in the model); ${\beta }_j$ refers to the regression coefficient on the jth lag of freshmen enrollment (e.g., ${\beta }_2$ refers to the coefficient for freshmen enrollment 2 years ago, $X_{i,t-2}$ ).

Distributed-lag models yield several testable hypotheses about the relationship between freshmen enrollment and faculty employment. If no lagged values of freshmen enrollment are included in the model (i.e., $L=0$ ), the null hypothesis of interest is $H_0\left(L=0\right):{\beta }_0=0$ , which assesses the relationship between freshmen enrollment in year $t$ and faculty employment in year $t$ . If lagged values of freshmen enrollment are included (i.e., $L>0$ ), then hypotheses about the relationship between specific lags of freshmen enrollment (e.g., $j=2$ ) and faculty employment can be tested. Like most distributed-lag analyses (e.g., Dell et al., [25]), we are interested in the cumulative relationship between freshmen enrollment and faculty employment rather than the relationship in a specific time period. This cumulative relationship can be estimated as the summation of coefficients from all lagged values of freshmen enrollment in the model, $\sum _{j=0}^L{\widehat{\beta }}_j$ . In turn, the null hypothesis that the cumulative relationship between freshmen enrollment and faculty employment equals zero is:

5 $$H_0\left(L>0\right):\sum _{j=0}^L{\beta }_j=0$$

Graph

The choice about the number of lags to include in the model can be informed by theory or by statistical tests (e.g., Akaike information criterion) (Parker, [56]). Following standard practice for distributed-lag models, all models included the current value of freshmen enrollment. Our conceptual discussion suggested time lags as long as 2 years for the relationship between freshmen enrollment, $X_{i,t-j}$ , and tenure line hires, $Y_{\mathit{it}}$ . We present distributed-lag models with $L=0$ (i.e., include $X_{\mathit{it}}$ ), $L=1$ (i.e., include $X_{\mathit{it}}$ and $X_{i,t-1}$ ), and $L=2$ (i.e., include $X_{\mathit{it}}$ , $X_{i,t-1}$ , and $X_{i,t-2}$ ).[2]

Conceptually, the relationship between nonresident enrollment and faculty employment is composed of an exogenous, reactive component and an endogenous, strategic component. The exogenous component is the relationship between faculty employment and an unanticipated change in enrollment demand. The endogenous component is variation in nonresident enrollment due to purposeful enrollment behavior. Decisions about enrollment goals and enrollment management behavior may be made in concert with decisions about faculty hiring, such that variation in enrollment and faculty employment is at least partially jointly determined.

Ideally, analyses would estimate the causal relationship between enrollment and faculty employment because causal relationships are often more helpful than correlational relationships for planning and policy purposes. Estimates of the causal effect of enrollment on faculty employment would be based on "reactive variation" in enrollment that is exogenously determined, which is akin to randomly assigning levels of enrollment demand. Causal estimates would exclude "strategic variation" in nonresident enrollment due to purposeful enrollment management behavior. Because we do not isolate exogenous variation in enrollment (e.g., an experiment or an instrumental variables approach), our models estimate how faculty employment correlates to changes in nonresident enrollment that are driven by the combination of successful enrollment management efforts and unanticipated changes in nonresident demand. The joint decision that higher education institutions make to both hire faculty and manage their enrollment renders the coefficients estimated in this study as correlational, and not causal. However, we seek to get closer to causal estimates by attempting to minimize potential unobserved confounding factors that lead to spurious correlations.

To understand the primary threats to internal validity, we describe the two assumptions that must be satisfied to interpret the estimates $\sum _{j=0}^L{\widehat{\beta }}_j$ as causal effects. First, the "random effects" assumption states that there is no relationship between independent variables of interest, $X_{i,t-j}$ , and the institution-varying, time-invariant omitted variables, ${\alpha }_i$ , that affect faculty employment. Second, the "strict exogeneity" assumption states that there is no relationship between $X_{i,t-j}$ and institution-varying, time-varying omitted variables, ${\epsilon }_{\mathit{it}}$ , in any time period, $t=1,...,T$ , after controlling for covariates. Institution-level fixed effects satisfy the random affects assumption. We utilize the "within" fixed effects estimator, which satisfies the random effects assumption by subtracting the panel-level mean from each variable. This transformation eliminates all observed and unobserved (i.e., ${\alpha }_i$ ) institution-varying, time-invariant variation. Similarly, we control for omitted variables that vary across time but not across institutions by including dichotomous indicator variables for each time period, ${\delta }_t$ .

After the inclusion of institution and year fixed effects, the primary threat to unbiased estimates of causal effects is violation of the strict exogeneity assumption. In particular, we are concerned that the relationship between freshmen enrollment and faculty employment may be driven by institution-varying, time-varying variables which have been omitted from the model. Therefore, we attempt to minimize violations of strict exogeneity through the inclusion of time-varying, unit-varying covariates, $W_{\mathit{it}}$ , that plausibly (1) affect $Y_{\mathit{it}}$ and (2) have a relationship with $X_{\mathit{it}}$ . Our list of covariates, described below, attempts to control for determinants of faculty employment identified by labor demand theory. However, our results cannot be interpreted as causal because it is unlikely that all sources of omitted variable bias can be eliminated through the inclusion of covariates (Hoxby, [37]).

In order to appreciate the strengths and limitations of our methodological approach, we discuss the sources of variation in freshmen enrollment—focusing on nonresident freshmen—and what variation our coefficients capture. Year-to-year changes in nonresident freshmen enrollment at university $i$ are driven by "plausibly exogenous" changes in nonresident student demand and by purposeful enrollment management behavior. Drawing from prior research (e.g., Cooke & Boyle, [22]; Zhang, [67]; Zhang & Ness, [70]), nonresident student demand at university $i$ is partially determined by changes in nearby states, including enrollment capacity of public research universities, in-state tuition price, state merit aid expenditure, and the adoption of "top 10%" plans. These factors are plausibly exogenous in that they affect the number of nonresident students that want to attend university $i$ , but university $i$ cannot control them. University enrollment management behaviors designed to increase nonresident enrollment are endogenous because university $i$ directly controls enrollment management behavior and faculty employment.

We constructed a panel dataset of public research universities using data from the Integrated Postsecondary Education Data System (IPEDS). We supplemented this data with county-level employment measures from the U.S. Census.

The analysis sample was the population of 136 public research universities that (1) enroll undergraduate students and (2) were defined as "very high" or "high" research activity according to the 2005 Carnegie Classification. We restricted the sample to public research universities because prior research suggests that the majority of public "master's" universities and "baccalaureate" colleges cannot grow substantial nonresident enrollment due to weak student demand (Jaquette & Curs, [41]; Zhang, [67]). We used 2005 Carnegie Classification because this iteration was closest to the beginning of our analysis period.

The analysis period was 2002–2003 through 2016–2017. The start and end of the analysis period was determined by variable availability. Nevertheless, this period is particularly poignant for our research. It encompasses a sharp decline in state appropriations following the 2008 recession, which shifts university budget constraints inward, and also a prolonged period of nonresident enrollment growth.

All variables are measured in levels, rather than logs, to facilitate comparison between the coefficients on resident and nonresident enrollment. Although coefficients on logged values can be interpreted as elasticities, for most universities a 1% increase in nonresident enrollment is a much smaller number of students than a 1% increase in resident enrollment. All covariates (except for primary independent variables of interest—resident and nonresident enrollment) are lagged by 1 year to reduce the likelihood of endogeneity bias (we assume that levels in year $t-1$ are likely to have the strongest relationship with faculty employment outcomes in year $t$ ).

Missing institution-year observations for the dependent variables and key independent variables were not imputed. For covariates, missing institution-year observations (year t) were imputed using the average of the within-panel 1-year lag (year t–1) and the lead (year t + 1) observations. For the analytical samples, 235 observations (13.3%) in the full-time faculty hires samples and 252 observations (12.7%) in the part-time faculty employment sample contained missing values for at least one covariate.

The three dependent variables are the number of tenure line faculty hires, the number of full-time NTT faculty hires, and the total employment of part-time NTT faculty.

Our decision to model hires for the full-time faculty outcomes has conceptual and methodological advantages over panel analyses of faculty employment, such as Zhang et al. ([68]). Conceptually, we want to know whether the size of the faculty labor force is correlated with changes in enrollment. For tenure line faculty and for full-time NTT faculty on multi-year contracts, total employment in time $t$ is largely dictated by employment in time $t-1$ because these faculty cannot be laid off in a given year. Therefore, year-to-year variation in total employment is modest, depending on the combination of new hires and departures (e.g., retirement, move to a new university) in a given year. Furthermore, modeling hires is conceptually desirable because hires in time $t$ is not dictated by hires in time $t-1$ . Therefore, universities may substantially adjust the number of hires in response to changes in enrollment. Additionally, new hires are a cleaner measure because it is composed of one underlying construct. By contrast, total faculty employment is an amalgamation of several constructs (e.g., employment last year, retirements, new hires).

Methodologically, panel models of faculty employment should include lagged faculty employment because employment this year is systematically determined by faculty employment last year. When lagged dependent variables are included in fixed effects panel models, the data transformation process that removes unit-varying, time-invariant variation creates systematic correlation between regressors and the error term and generates inconsistent estimates (Nickell, [55]). Overcoming this bias requires an instrumental variables estimator, such as the Arellano-Bond estimator, which is more sensitive to model specifications and make stronger statistical assumptions. By contrast, models of new hires are methodologically cleaner because they do not require the inclusion of lagged measures of new hires.

The IPEDS Human Resources survey component has collected data on full-time new hires on an annual basis since Fall 2001. Throughout the analysis period, full-time tenure line and full-time lecturer new hires were defined as full-time employees with faculty status. However, institutions have discretion in how they define faculty status.[3]

Conceptual definitions and reporting requirements in the survey instrument have changed somewhat over time. With respect to definitions, the IPEDS Human Resources survey was substantially redesigned starting with data collected in Fall 2012. Prior to redesign, the New Hires sub-component asked institutions to count the number of full-time employees hired whose primary occupation included instruction and/or research and/or public service. After redesign, institutions were asked to count the number of full-time "instructional staff" employees hired. The concept "instructional staff" is defined as "all individuals whose primary occupation includes instruction" (National Center for Education Statistics, [54]), thereby consisting of staff "who are either: (1) primarily Instruction or (2) instruction combined with research and/or public service" (National Center for Education Statistics, [54]). Thus, prior to redesign, the measures of full-time tenure line and full-time lecturer new hires included employees whose primary occupation included research and/or public service but did not include instruction.

With respect to reporting requirements, from Fall 2001 through Fall 2014, reporting new hires data was required in odd years (e.g., Fall 2001, Fall 2003) and optional in even years (e.g., Fall 2002, Fall 2004). Starting in Fall 2015, reporting new hires data was required in all years. Finally, from Fall 2001 through Fall 2015, institutions were asked to report full-time staff hired in the 4-month period between July 1 and October 31. Starting in Fall 2016, institutions were asked to report full-time staff hired in the 12-month period starting November 1 of the previous calendar year through October 31 of the current calendar year. The inclusion of year indicators accounts for changes in measure definition that affect all institutions.[4]

The IPEDS Human Resources component does not collect data on part-time NTT faculty hires. Therefore, we model the total annual employment of part-time NTT faculty. We assume that models of part-time NTT faculty employment do not need to include lagged values of part-time NTT faculty employment. Our rationale is that most part-time faculty do not have multi-year contracts (Anderson, [3]). Therefore, employment in year $t$ is not dictated by employment in year $t-1$ . For all years of the analysis period, the measure is defined as all part-time staff whose primary occupation includes instruction and/or research and/or public service. This measure includes staff with and without faculty status and includes tenure line and non-tenure track staff.

We model three independent variables of interest: (1) full-time resident freshmen enrollment; (2) full-time nonresident freshmen enrollment; and (3) full-time freshmen enrollment defined as the sum of resident and nonresident enrollment. Our primary interest is comparing the coefficients on the resident and nonresident enrollment. We first estimate models of total full-time freshmen enrollment to examine whether coefficient direction and magnitude seem reasonable. Because undergraduate tuition revenue is a function of total enrollment rather than freshmen enrollment, we would also like to create measures of total resident and total nonresident enrollment. However, measures of enrollment by residency status are collected only for freshmen.

These three measures were derived from the IPEDS Student Financial Aid survey component, which collects data about full-time freshmen students. We defined resident full-time freshmen as the sum of students paying in-district and in-state rates. We defined nonresident freshmen as the number of students paying out-of-state rates. Thus, the resident and nonresident enrollment constructs are aligned with what tuition a student pays (in-state vs. out-of-state) as opposed to their actual residence. This dichotomy includes international students who are classified as resident or nonresident based upon the tuition that they pay.

The IPEDS Student Financial Aid survey reported a nonzero number of students with unknown residency status. For example, in 2017 the University of Utah reported enrollment of 2,231 resident freshmen, 958 nonresident freshman, and 130 freshmen of unknown residency. When the number of freshmen of unknown residency was greater than zero, we distributed the enrollment with unknown residency based upon the average residency percentages within the institution from the previous and subsequent years. If both the previous and subsequent years were not available, imputation was based upon the previous year only and then the subsequent year only. We imputed enrollment by residency for 152 observations (8.6%) in the full-time faculty hires samples and 176 observations (8.9%) in the part-time faculty employment sample. Models in which imputed values of resident and nonresident enrollment were dropped are shown in the sensitivity analyses section.

To reduce violations of the strict exogeneity assumption, we include institution-varying, time-varying covariates that plausibly affect faculty employment outcomes and have a relationship with the independent variable of interest. Our rationale for covariate inclusion is based on labor demand theory, specifically Eq. (2) which derived the demand determinants for a particular faculty contract type by universities. Conceptually, we categorize the determinants of Eq. (2) as relative wages (represented by $w_c,w_c^{\prime }$ in Eq. 2), operating revenues from tuition ( $P_e,Q_e$ ), operating revenues from research ( $P_r,Q_r$ ), and subsidy revenues ( $S$ ).

Labor demand theory states that university demand for a faculty contract type (e.g., tenure line faculty) decline when wages increase and when wages of substitute labor decrease (e.g., full-time NTT faculty). All models control for the following measures of average salary at university $i$ in time $t-1$ : full-time tenured full professor; full-time tenure line assistant professor; and full-time NTT faculty. IPEDS does not collect data on the salaries of part-time NTT faculty. In lieu, to control for economic factors related to the relative wage for NTT faculty and other economic factors related to faculty employment we control for unemployment rate and median income within the institution's county.

Our theoretical model assumes that public research universities sell two products, enrollment, at quantity $Q_e$ , and research, at quantity $Q_r$ . Tuition revenue—defined in Eq. (1) as the product of quantity of students, $Q_e$ , and tuition price $P_e$ —is operating revenue universities receive to enroll students. Our theoretical model suggests that enrollment affects university demand for faculty by shifting out the budget constraint and by increasing direct labor and capital costs.

This paper seeks to compare whether faculty hiring correlates differently with growth in resident freshmen versus growth in nonresident freshmen, motivated by the idea that the marginal nonresident student generates more tuition revenue than the marginal resident student. Therefore, we should control for other components of quantity of students, $Q_e$ , and tuition price, $P_e$ , because these variables likely affect faculty employment and may have a systematic relationship with resident and nonresident freshmen enrollment.

We control for the price of resident undergraduate tuition and the price of nonresident undergraduate tuition. We also control for average institutional grant aid awarded to full-time freshmen, which affects net tuition revenue from undergraduate students. Since our measures of resident and nonresident freshmen enrollment include full-time students only, we control for the number of part-time freshmen. At the graduate level, we control for the number of full-time equivalent graduate and professional students and also in-state and out-of-state graduate tuition prices.

Over the past decade, policymakers in several states are pressuring public research universities to enroll more transfer students from in-state community colleges (e.g., California Community Colleges & University of California, [16]; Gordon, [35]). IPEDS began collecting annual data on the number of undergraduate transfers in 2008. Our main models do not include a measure of transfer enrollment because doing so would shorten our analysis period to cover only 2007–2008 through 2016–2017. However, we present models that control for transfer enrollment in the sensitivity analysis section.

Operating revenues from the production of research—defined in Eq. (1) as the product of quantity of research, $Q_r$ , and the price of research, $P_r$ —affects university demand for faculty. First, research revenues shift out the budget constraint available for hiring faculty. Second, research funding must be expended on capital and labor costs—including faculty and research staff—necessary to produce the promised deliverables. Further, growth in research funding could plausibly be related to resident and nonresident enrollment. Therefore, we should control for measures of the scale of research output related to research operations. Specifically, we control for federal operating grant and contract revenues (e.g., NSF research funding), state operating grant and contract revenues (e.g., research funding from a state agency), and private operating grant and contract revenues (e.g., research funding from a private foundation).

Beyond the core operations of producing graduates and research, we also control for measures of other operating outputs that may generate revenues to hire faculty and may require faculty labor to produce. Specifically, we control for hospital revenues and revenues from independent operations.

Subsidy revenues increase the budget constraint available to hire faculty but do not necessarily increase expenditure on specific labor and capital costs because subsidy revenues are not tied to the production of a particular product. Further, subsidy revenues may have a systematic relationship with resident and/or nonresident enrollment. For example, Jaquette and Curs ([41]) found that state appropriations had a strong negative relationship with nonresident enrollment. We control for state appropriations, federal appropriations, and revenue from private donations. We also control for the beginning year market value of the university endowment, based on the idea that universities annually expend some percentage of their endowment to support operations.

Table 1 presents descriptive statistics for the respective samples of each dependent variable and the independent variables of interest. Annually, the average institution in our sample hired 39 new full-time tenure line faculty and 49 full-time non-tenure line faculty. Figure 2 demonstrates that mean full-time faculty hires declined following the 2008 recession for both tenure line and NTT faculty.[5] Although NTT faculty hiring rebounded more quickly, tenure line hires increased steadily since 2009–2010.

Table 1 Descriptive statistics for the analytic samples, 2003–2017

Graph: Fig. 2 Mean full-time tenure line and full-time NTT faculty hires, 2002–2003 to 2016–2017. Data is reported for years in which the new hires data collection in IPEDS was mandatory. Prior to 2013, faculty were defined as those whose primary occupation included instruction and/or research and/or public service. After 2013, faculty were defined as all individuals whose primary occupation includes instruction. Prior to 2016, full-time faculty hires were counted across the 4-month period July 1 to October 31. After 2016, full-time faculty hires were counted for the 12-month period November 1 to October 31

The average institution in our sample employed 524 part-time NTT faculty across our sample. The bottom panel of Fig. 1 demonstrates that the utilization of part-time NTT employment has steadily risen across time, with a roughly 33% increase between 2002–2003 and 2016–2017.

The average institution in our analytic sample (based upon the full-time tenure line analysis sample) annually enrolled 3755 freshmen, of which 2904 were residents and 851 were nonresidents. Figure 3 demonstrates that freshmen enrollment in the analytical sample steadily increased across time, with a larger percentage increase for nonresident freshmen.

Graph: Fig. 3 Mean full-time freshmen enrollment by tuition residency status, 2002–2003 to 2016–2017

Table 2 presents the estimated results from distributed lag fixed effects models examining the relationship between total freshmen enrollment and full-time tenure line faculty hires. Column (1) includes only contemporaneous total freshmen (i.e., L0. Total freshmen), column (2) includes contemporaneous total freshmen and 1-year lagged total freshmen (i.e., L1. Total freshmen), and, column (3) includes contemporaneous, 1-year lagged, and 2-year lagged total freshmen (i.e., L2. Total freshmen). All models are estimated with robust standard errors—to relax the assumption of homoscedasticity—and clustered at the institution-level—to relax the assumption of no serial correlation between observations within institutions.

Table 2 The relationship between total freshmen enrollment and tenure line faculty hires

Robust standard errors clustered at the institution-level in parentheses List of lagged covariates include: average salary for full-time tenured full professors, average salary for full-time tenure line assistant professors, average salary for full-time NTT faculty, county-level unemployment rate, county-level median income, resident undergraduate tuition, nonresident undergraduate tuition, average institutional grants to full-time freshmen, part-time freshmen enrollment, resident graduate tuition, nonresident graduate tuition, enrollment of full-time equivalent graduate students, federal operating grant and contract revenues, state operating grant and contract revenues, private operating grant and contract revenues, hospital revenues, independent operations revenues, state appropriations, federal appropriations, private donation revenues, university endowment market value ***p < 0.01, **p < 0.05, *p < 0.1 aAll enrollment variables are scaled to represent 100 students

The results from the contemporaneous model show that a within institution increase of 100 freshmen was associated with an increase of 0.67 full-time tenure line faculty hires. The addition of lagged freshmen enrollment to the model demonstrated that hiring patterns for full-time tenure line faculty occur over a number of years rather than at one particular time period. When including a 1-year lag, the results indicate that a within institution increase of 100 freshmen was associated with an increase of 0.35 full-time tenure line hires in the contemporaneous year and 0.50 full-time tenure line hires in the subsequent year, yielding a total of 0.85 new hires. When adding second-year lagged enrollment to the model, the results indicated that full-time tenure line hiring is relatively spaced across the 3-year period, 0.32 in the contemporaneous year, 0.34 in the lagged year, and 0.29 in the second-lagged year, for a total of 0.94 new hires.

Table 3 presents the results when freshmen enrollment was separated by resident and nonresident students. For resident freshmen enrollment, the association with full-time tenure line new faculty hiring appears to have been contemporaneous, as all coefficients on lagged enrollment terms were insignificantly different from zero and the total relationship only marginally increased from 0.54 to 0.64 when lagged enrollment was included. Interestingly, this could indicate that higher education institutions are able to accurately project resident enrollment as associated hiring occurred contemporaneously. Overall, the results would suggest that a within institution increase of 100 freshmen was associated with a total increase of 0.64 full-time tenure line faculty hires.

Table 3 The relationship between resident and nonresident freshmen enrollment and tenure line faculty hires

Robust standard errors clustered at the institution-level in parentheses See Table 2 for list of included covariates ***p < 0.01, **p < 0.05, *p < 0.1 aAll enrollment variables are scaled to represent 100 students

For nonresident enrollment, the estimated association with full-time tenure line faculty hires was stronger and appeared to be delayed by 1 year. Specifically, the association between enrollment and full-time tenure line hires was strongest in the first-lagged year. The 2-year distributed lag models estimated that a within institution increase in nonresident enrollment of 100 freshmen was associated with a 1.42 increase in full-time tenure line faculty hires. The sum of coefficients for nonresident enrollment in the 1- and 2-year lag models were found to be over twice the magnitude (p < 0.1) when compared to the sum of coefficients for resident enrollment.

Table 4 presents estimates of the association of total freshmen enrollment and full-time NTT faculty hiring. For each of the distributed lag models, only the coefficient on contemporaneous enrollment was statistically significant, indicating that full-time non-tenure line faculty hiring was contemporaneous in nature. Specifically, a within institution increase of 100 total freshmen was associated with a contemporaneous increase of 0.65 full-time non-tenure line faculty hires. Point estimates of the total association (including 1- and 2-year lagged enrollment) ranged from 0.55 to 0.68 although model fit declined when including additional lagged enrollment terms.

Table 4 The relationship between total freshmen enrollment and full-time non-tenure track faculty hires

Robust standard errors clustered at the institution-level in parentheses See Table 2 for list of included covariates **p < 0.05, *p < 0.1 aAll enrollment variables are scaled to represent 100 students

Table 5 presents estimates of the association of resident and nonresident freshmen enrollment and full-time NTT new faculty hiring. The results indicate that there is no statistically significant difference in the association between the hiring of full-time NTT faculty for resident and nonresident enrollment.

Table 5 The relationship between resident and nonresident freshmen enrollment and full-time non-tenure track faculty hires

Robust standard errors clustered at the institution-level in parentheses See Table 2 for list of included covariates *p < 0.1 aAll enrollment variables are scaled to represent 100 students

Table 6 presents estimates of the association of total freshmen enrollment and part-time NTT faculty employment. Similar to the full-time NTT models, for each distributed-lag model, contemporaneous freshmen enrollment was the only coefficient significantly related to part-time NTT faculty employment. Specifically, a within institution increase of 100 total freshmen was associated with a 5.5 increase in part-time NTT faculty. Point estimates of the total association (including 1- and 2-year lagged enrollment) ranged from 5.5 to 6.9, with model fit indices being similar across specifications. These results suggest that freshmen enrollment growth was correlated with immediate increases in the employment of part-time NTT faculty. Although coefficient magnitudes were much larger in part-time NTT faculty models when compared to full-time tenure line models, these coefficients should not be interpreted directly for two reasons. First, hires and employment are fundamentally different measures. Second, the part-time NTT hires are not adjusted to full-time equivalency.

Table 6 The relationship between total freshmen enrollment and part-time non-tenure track faculty employment

Robust standard errors clustered at the institution-level in parentheses See Table 2 for list of included covariates ***p < 0.01, **p < 0.05 aAll enrollment variables are scaled to represent 100 students

Table 7 presents estimates of the association of resident and nonresident freshmen enrollment and part-time NTT faculty employment. In general, there was no statistically significant difference in the association of resident or nonresident freshmen enrollment to part-time NTT faculty employment. However, the timing of part-time NTT faculty employment follows the same pattern as full-time tenure line hiring, as the association with resident enrollment was contemporaneous and the timing with nonresident enrollment appeared to be lagged 1 year.

Table 7 The relationship between resident and nonresident freshmen enrollment and part-time non-tenure track faculty

Robust standard errors clustered at the institution-level in parentheses ***p < 0.01, **p < 0.05, *p < 0.1 See Table 2 for list of included covariates aAll enrollment variables are scaled to represent 100 students

Several robustness checks were estimated to investigate the sensitivity of the results to alternative model specifications and data imperfections.

As described in the data and variables section, IPEDS reported a nonzero percentage of students with unknown residency status (e.g., resident vs. nonresident) for 152 observations (8.6%) in the full-time faculty hires samples and 176 observations (8.9%) in the part-time faculty sample. In all models previously presented, we included observations that were imputed following the procedures previously described. Table 8 compares the previously reported two-lag distributed-lag models for each dependent variable. Specifically, columns (1), (3), and (5) present coefficient estimates for models that do not include imputed enrollment data, and columns (2), (4), and (6) present specifications with imputed enrollment data. The results were robust across all three dependent variables, with point estimates well within 95% confidence intervals.

Table 8 Sensitivity of empirical models to exclusion of observations with unknown residency

Robust standard errors clustered at the institution-level in parentheses See Table 2 for list of included covariates ***p < 0.01, **p < 0.05, *p < 0.1 aAll enrollment variables are scaled to represent 100 students

The previously presented models are potentially missing an important construct—transfer student enrollment—because IPEDS did not begin data collection on transfer students until the 2007–2008 academic year. The exclusion of transfer students from our models has the potential to positively bias the coefficients on both resident and nonresident enrollment, as transfer student growth is likely positively correlated to enrollment, and labor demand theory predicts it is a positive determinant of faculty hiring.

To investigate the sensitivity of the omission of transfer student enrollment, Table 9 presents estimates of the two-lag distributed-lag models which exclude—columns (1), (3), and (5)—and include—columns (2), (4), and (6)—the transfer enrollment variable. For consistency, the samples for each specification are restricted to the time period for which the transfer enrollment variable is available (2008–2017). The results were robust across all three dependent variables, with alternative estimates well within 95% confidence intervals.

Table 9 Sensitivity of empirical models to inclusion of transfer enrollment control variable

Robust standard errors clustered at the institution-level in parentheses See Table 2 for list of included covariates ***p < 0.01, **p < 0.05, *p < 0.1 aAll enrollment variables are scaled to represent 100 students

Declines in state appropriations have decreased the ability of public research universities to hire faculty, particularly tenure line faculty (Ehrenberg, [27]; Frye, [32]; Kane & Orszag, [44]), and compelled universities to grow nonresident enrollment as a substitute for state funding (Jaquette & Curs, [41]). Policymakers have criticized nonresident enrollment growth as antithetical to the mission of public universities, and several states adopted or are considering nonresident enrollment caps. This paper attempts to analyze whether faculty hiring by public research universities was associated differently with nonresident versus resident freshmen enrollment growth.

We modeled three dependent variables—full-time tenure line faculty hires, full-time NTT faculty hires, and part-time NTT faculty employment. We employed a fixed effects panel model estimation strategy, which reduced omitted variable bias due to institution-varying, time-invariant omitted variables. We attempted to minimize violations of strict exogeneity by including institution-varying, time-varying covariates motivated by labor demand theory.

Our coefficient estimates were based on variations in freshmen enrollment that are due to changes in student demand and due to university enrollment management behavior. These estimates are not causal because enrollment management behavior is endogenous. However, these estimates may have more policy relevance than a causal estimate. Prior research suggests that long-term, nonresident enrollment growth is substantially driven by enrollment management behaviors (e.g., institutional aid policy, recruiting behavior, admissions policy) that may require several years to fully implement (Burd, [15]; Leeds & DesJardins, [48]; Salazar et al., [61]). Universities may be implementing a long-term strategy to increase faculty hiring by enrolling more nonresident students. Our models capture the relationship between successful efforts to increase nonresident enrollment and faculty hiring. By contrast, a causal estimate based on unanticipated, exogenous variation in student demand would not.

We found a strong, positive relationship between total freshmen enrollment growth and full-time tenure line faculty hires. It was estimated that an increase of 100 freshmen within an institution was associated an increase of 0.9 full-time tenure line hires across the subsequent 3 years. Models that disaggregated freshmen enrollment found a larger relationship for nonresident enrollment when compared to resident enrollment. Specifically, an increase of 100 nonresident students was associated with hiring 1.4 more full-time tenure line faculty, compared to only 0.6 full-time tenure line hires given an increase of 100 resident freshmen. Interestingly, nonresident enrollment growth was associated with increased full-time tenure line hiring across a 3-year period while resident enrollment growth was associated with contemporaneous hiring. In contrast, for full-time NTT faculty hires, there was not a statistically significant association with total, resident, or nonresident freshmen enrollment.

Models of part-time NTT employment found positive, significant coefficients for total freshmen, resident freshmen, and nonresident freshmen. For all three measures of freshmen enrollment, coefficient magnitudes were quite similar and was driven primarily by current-year freshmen enrollment. These results suggest freshmen enrollment growth was correlated with increased part-time faculty employment the same year these freshmen arrive on campus, regardless of whether enrollment growth is driven by resident or nonresident students.

Our results contribute to scholarship on the determinants of faculty employment. Whereas prior panel analyses model faculty employment (e.g., Brown et al., [14]; Zhang et al., [68]), we model faculty hiring, which is conceptually and methodologically cleaner. More substantively, public universities are increasingly tuition reliant, but prior analyses model total FTE enrollment (e.g., Zhang et al., [68]) rather than disaggregating enrollment by tuition price. In particular, labor demand theory suggests that nonresident and resident enrollment have different effects on the budget constraint, and we find that universities hire more tenure line faculty in response to nonresident enrollment growth than in response to resident enrollment growth.

Our results can inform institutional policy decisions. University administrators argue that, amidst state budget cuts, nonresident enrollment growth enables universities to finance resident access and faculty hiring (e.g., Peacock, [57]). For example, in a newspaper article about nonresident enrollment growth at the University of Michigan, Provost Pollack stated that "'during the great recession we were able to hire a lot of great faculty members'" (Allen, [1]). Our analyses do support the claim that nonresident enrollment growth is associated with hiring more tenure line faculty. Further, the magnitude of this relationship was significantly larger than that of resident enrollment. The institutional policy implication is that nonresident enrollment growth may be a viable strategy to finance tenure line faculty hires. However, administrators should be aware that prior research suggests that nonresident enrollment growth reduces the percentage of Pell recipients and underrepresented students of color (Jaquette et al., [42]), potentially exacerbating socioeconomic and racial isolation on campus.

Our results can also inform state policy decisions. Historically, tenure line faculty at public universities were subsidized by state appropriations (Kane & Orszag, [44]). Although most universities allocate the majority of revenue from state appropriations and tuition to the same "general funds" budget (Ehrenberg, [26]), it is not a given that nonresident tuition revenue will be spent on faculty personnel costs. Our results suggest that, at universities with strong nonresident enrollment, state funding cuts will not devastate the ability of universities to hire tenure line faculty.

At the same time, our results caution against state policies that simultaneously cut funding and cap nonresident enrollment. While this policy stance may be fiscally and politically attractive, it would preclude universities from generating revenue necessary to hire and retain quality faculty. Therefore, we argue that any nonresident enrollment cap policies should be tied to states meeting an agreed-upon "adequate" funding threshold. This way, state universities have a responsibility to focus on state residents if states fulfill their responsibility to finance state universities. Finally, state policymakers should recognize that many public research universities and most "regional" public universities face weak nonresident enrollment demand (Jaquette & Curs, [41]). These universities are unable to compensate for declines in state funding by growing nonresident enrollment.

As a complement to this study, we recommend that future research examine the effect of nonresident enrollment on university expenditures aside from faculty personnel. Nonresident students tend to be more affluent than residents and prior research finds that affluent students have stronger preferences for consumption amenities (e.g., luxury dorms and recreational facilities, big-time college sports, student activities) that do not directly benefit quality of education (Armstrong & Hamilton, [7]; Jacob et al., [38]). Future research should analyze the effect of nonresident enrollment on operating expenditures by category (e.g., instruction, auxiliary, student affairs) and on expenditure on facilities construction.

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