STUDIES IN APPLIED MICROECONOMICS
By
JAMES F. DEWEY
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1998
ACKNOWLEDGEMENTS
I owe much to my teachers. Sunne Brandemeyer piqued my interest in economics when I
took Principles of Microeconomics as a sophomore. Phil Porter inspired my interest in public
policy and public choice. Jon Hamilton and Steve Slutsky taught me the fundamentals of
microeconomic theory and were always available as members of my committee. I was lucky to
have Wayne Francis as the outside member of my committee. I am especially grateful to the
cochairmen of my committee, Larry Kenny and David Sappington, for their wise counsel and
friendly support.
I would also like to thank Chunrong Ai, Sanford Berg, Tracy Lewis, Megan Werner, and the
late Ed Zabel for knowledge imparted in classes and numerous other useful discussions. Dave
Denslow, Mark Jamison, Rich Romano, and Ragiv Sharma provided many useful comments on
my research. Financial support from the Public Policy Research Center at the University of
Florida is also gratefully acknowledged.
TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS ii
ABSTRACT v
CHAPTERS
1 INTRODUCTION 1
2 MORE IS LESS? REGULATION IN A RENT SEEKING WORLD 4
Introduction 4
The Model 6
Central Findings 13
Conclusion 23
3 DETERMINING THE RULES OF THE GAME:
REGULATORY REGIME ADOPTION IN THE U.S.
TELECOMMUNICATIONS INDUSTRY 25
Introduction 25
A Simple Model of Regulatory Regime Adoption 28
The Empirical Model 43
Conclusion 58
4 THE INEFFECTIVENESS OF SCHOOL INPUTS:
A PRODUCT OF MIS SPECIFICATION? 61
Introduction 61
The Statistical Effects of Including Demand Variables 65
MetaReanalysis of the Education Production Function Literature 69
Estimating Production Functions: Sensitivity to Specification 78
Conclusion 97
5 CONCLUSION 100
APPENDIX A
APPENDIX B
page
PROOFS OF PROPOSITIONS IN CHAPTER 2 106
EMPIRICAL STUDIES YIELDING DATA USED
IN THE META ANALYSIS IN CHAPTER 4 110
REFERENCES 114
BIOGRAPHICAL SKETCH 121
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
STUDIES IN APPLIED MICROECONOMICS
By
James F. Dewey
December 1998
Chairman: Lawrence W. Kenny
Cochairman: David E. M. Sappington
Major Department: Economics
My dissertation applies microeconomics in the areas of regulation and education. Chapter 2
examines a theoretical model of competition between heterogeneous interest groups in a
regulatory environment. The following are three of my results. First, a change that enhances
gross surplus may reduce expected net welfare. Second, the group that finds it more costly to
lobby for a favorable decision benefits more from an increase in its opponent's marginal cost of
exerting pressure than from an equal reduction in its own marginal cost of lobbying. Third,
requiring a regulated firm to share some of its profits with consumers reduces lobbying
expenditures, improves consumer welfare, and may even increase the firm's welfare.
Chapter 3 uses a simple theory of the political economy of regulation to explain why states
choose different types of regimes to regulate intrastate telecommunications. States in which the
gains to enhanced efficiency are larger or uncertainty is lower are more likely to adopt
alternative regulatory forms designed to enhance efficiency. States where lobbying or
negotiation costs are higher are more likely to employ some form of earnings sharing, in accord
with the theoretical result that profit sharing reduces lobbying costs. I also find that the relative
political strengths of consumers and the firm have significant impacts on regime adoption.
A large number of academic studies have found that school inputs, such as teacher education,
class size, or simply expenditures per pupil, are not systematically related to improved academic
performance. Chapter 4 examines the possibility that two common forms of model
misspecification drive these findings. I review existing studies and classify them as
"misspecified" if they exhibit one of these two potential flaws. Using meta analysis I find that
studies that are not "misspecified" show strongly significant positive relationships between
school inputs and achievement. Further, the "misspecified" studies are significantly less likely to
find that school inputs matter. Direct comparisons achieved by analyzing the same data set using
both the erroneous methodology and the suggested methodology add support for my claims.
CHAPTER 1
INTRODUCTION
Microeconomic analysis can shed light on a number of interesting areas of public policy.
The chapters that comprise my dissertation apply microeconomics in the important areas of
regulation and education. Chapter 2, "More is Less? Regulation in a Rent Seeking World,"
examines lobbying activity and welfare in a theoretical model of competition between
heterogeneous interest groups in a regulatory environment. Chapter 3, "Determining the Rules
of the Game: Regulatory Regime Adoption in the U.S. Telecommunications Industry,"
undertakes an empirical examination of the reasons that states employ different types of
regulatory regimes in their intrastate telecommunications industry. Chapter 4, "The
Ineffectiveness of School Inputs: A Product of Misspecification?," offers a critical appraisal of
the common empirical finding that increased public school inputs do not lead to higher academic
achievement and presents new evidence indicating that such findings are in error.
Chapter 1, "More is Less? Regulation in a Rent Seeking World" examines a model in which
two opposing groups compete for favorable regulatory decisions. The following are just three of
the more striking results that are proven in the paper. First, a change that enhances gross surplus
may reduce expected net welfare. If the change increases the groups' stakes in the decision, the
groups will exert more effort to win their preferred outcome. This increases rent seeking costs
and may reduce the likelihood that the outcome with the highest aggregate gross surplus is
implemented. These effects may outweigh the direct benefits of the increase in gross surplus.
Second, the group that finds it more costly to lobby for a favorable decision benefits more from
2
an increase in its opponent's marginal cost of exerting pressure than from an equal reduction in
its own marginal cost of lobbying. Thus, it is not surprising that proposals to limit special
interest influence, such as campaign finance reform, generate more popular attention than
proposals to increase the average citizen's participation. Since special interests probably find it
easier to exert pressure, the former course would be more beneficial to the average citizen and
more costly to special interests. Third, since rent seeking in this context can create significant
burdens, society may at times seek ways to reduce these political costs. Requiring a regulated
firm to share some of its profits with consumers reduces the stakes of the opposing groups by
partially aligning their interests. This reduces lobbying expenditures and improves consumer
welfare. The firm's welfare may also increase since the firm's direct loss from sharing is offset in
two ways; the firm incurs lower lobbying expenses and its opponent lobbies less.
Since the divestiture of the Bell System on January 1st, 1984, many states have adopted
alternatives to traditional rate of return regimes to regulate intrastate telecommunications,
ostensibly to provide enhanced incentives for efficient operation. Chapter 3, "Determining the
Rules of the Game: Regulatory Regime Adoption in the U.S. Telecommunications Industry" uses
a simple theory of the political economy of regulation, together with the basic differences in
incentives under the three most common regulatory alternatives rate of return regulation,
earnings sharing regulation, and price cap regulation  to explain regime adoption patterns
across states. States in which the gains to enhanced efficiency are larger or uncertainty is lower
are indeed more likely to adopt an alternative regulatory form. The relative political importance
of consumers and the firms also has significant impacts on regime adoption. Increases in
consumer strength tend to make price cap regulation less likely. Similarly, states where lobbying
or negotiation costs are higher are more likely to employ earnings sharing relative to price caps.
This finding is in accord with the theoretical result indicating that profit sharing reduces lobbying
costs.
Like any production process, the education of children requires inputs. These educational
inputs may be grouped into three types: school inputs, student inputs, and family inputs. A large
number of academic studies have found that school inputs, such as teacher education, class size,
or simply expenditures per pupil, are not systematically related to improved academic
performance. Chapter 4, "The Ineffectiveness of School Inputs: A Product of Misspecification?"
examines the possibility that two common forms of model misspecification may drive these
findings. First, some studies make no effort to control for family inputs. Second, some studies
use income, as opposed to parental education, time in the labor force, etc., to proxy family
inputs. This, however, creates problems. Income is a demand side variable that determines the
levels of all educational inputs but has no direct role in the production relationship. Even
assuming a recursive relationship, so that the OLS approach employed by almost all studies in
the literature is appropriate, including income instead of a more direct measure of family inputs
might increase collinearity, inflate standard errors, and lead to erroneous conclusions that school
inputs are irrelevant. I review existing studies and classify them as "misspecified" if they exhibit
one of these two potential flaws. Using meta analysis to combine information from the studies, I
find that studies that are not "misspecified" show strongly significant positive relationships
between school inputs and achievement. Further, the "misspecified" studies are significantly less
likely to find that school inputs matter. I also obtain two independent data sets and use both
"bad" and "good" methodology to analyze each of them. Each of the "good" analyses shows
much stronger impact of school resources on achievement than the corresponding "bad" study,
providing additional support for my claims.
CHAPTER 2
MORE IS LESS? REGULATION IN A RENT SEEKING WORLD
Introduction
Regulatory policy has changed substantially in a number of key industries in recent years.
The wave of deregulation that began in the 1970s and the use of profit sharing plans in
telecommunications regulation are important examples. Such policy changes are often spurred
by shifting market conditions or political conditions. The rapid development of new products
and new technologies in the telecommunications industry illustrates the first force. Efforts to
restrict contributions to political campaigns provide a striking example of the second.
Employing a model in which two opposing interest groups seek to influence the (binary) decision
of a standing regulator, I examine the impact of exogenous changes in economic conditions and
the cost of lobbying on regulatory outcomes. The analysis makes several new contributions to
the Economic Theory of Regulation (ET) pioneered by Stigler (1971).
The existing literature predicts that an increase in the potential surplus in a regulated market
will make at least one group better off, although the gains may be partially offset by increased
political competition. In contrast, my model shows that the political effects of such changes may
swamp the gross gains entirely, making all parties worse off. This can occur because the
increase in the available surplus may increase wasteful lobbying activity and also reduce the
likelihood that the regulator will make the decision leading to the largest (gross) social value.
Thus, changes in regulatory policy that increase the gross surplus available and could therefore
lead to Pareto improvements under ideal circumstances may in fact result in Pareto inferior
outcomes.
The prevailing literature also demonstrates that interest groups gain when the efficiency with
which they deliver political pressure increases. I extend the analysis to show that groups with a
high cost of delivering political pressure benefit more from an increase in their opponent's
lobbying costs than from an equal decrease in their own. This may help to explain why
campaign finance reform often generates more popular support than projects designed to increase
voter participation. If special interest groups generate pressure more efficiently than the general
population, limiting the power of the former may be the most effective way to improve the
welfare of the latter.
Attempts to explain deregulation using the ET have not always been successful. For
instance, Peltzman (1989) concludes that the ET does not explain the deregulation of trucking or
longdistance telecommunications. He reaches this conclusion because the beneficiaries of
regulation in those industries were still receiving substantial rents as a result of regulation at the
time of their deregulation. Since previous models of the ET indicated that regulation spread the
effects of changing conditions across all groups, insulating individual constituencies from
shocks, persistent rents implied the continued political viability of the existing regulatory system.
However, in the version of the ET represented by my model, the regulator will not always buffer
the effects of exogenous shocks. This difference points to a possible explanation of the
deregulation of these industries. In the period prior to deregulation, the rapid growth of trade
between geographically distant locations increased the demand for trucking and longdistance
telecommunications. This increased demand may have increased the stake of those opposed to
regulation (consumer surplus lost to regulation) enough relative to the stake of those favoring
continued regulation (profits generated by regulation) to overturn the existing system of
regulation.
Becker (1983) suggests that institutions may evolve to reduce the costs of political
competition. I show how profit sharing arrangements can serve this purpose. Profit sharing
partially aligns the interests of diverse groups, reducing lobbying activity. Further, profit sharing
unambiguously improves consumer and aggregate welfare. The direct costs to the firm (from
sharing its earnings) are dampened by the reduction in lobbying, and the firm's net profits may
even increase. These results suggest not only that profit sharing has beneficial welfare
properties, but also that it may be more likely to occur where political costs are high.
The remainder of the paper is organized as follows. The next section presents the model and
develops some preliminary results. The following section extends the model and presents the
primary findings of the paper. The final section concludes. Formal derivations and proofs of
propositions are relegated to an appendix.
The Model
There are two primary approaches to the study of questions of economic policy in a political
environment. The first stresses the platform choices made by candidates engaged in electoral
competition.1 The second stresses the policy choices made by a standing regulator or
government. While the first approach may provide important insights into the general direction
of public policy, the second seems better suited to the study of particular regulatory policies in
individual markets. Thus, the second approach has been most widely used to model the positive
political economy of regulatory policy, particularly by Stigler (1971), Peltzman (1976), Becker
1 AusinSmith (1997) provides a useful survey of public choice models of interest group activity.
(1983), and other works in the tradition of the ET.2 In addition to its widespread theoretical use,
a large body of empirical evidence supports the notion that the lobbying activities of interested
parties play a crucial role in the determination of regulatory policy.3 Accordingly, I follow
earlier works in the tradition of the ET and model regulatory outcomes as dependent upon the
lobbying activities of affected interest groups.
A binary decision is to be made by a regulatory authority; for example whether to allow
competition in a telecommunications market, to allow some expenditure into the rate base of an
electric utility, or to require a license to enter some profession. Two opposing groups seek to
influence the decision. It is perhaps easiest to envision one as a regulated firm and the other as a
group of large (industrial) consumers (e.g., a Wilson (1968) type syndicate). For example, a
2 The ET began in earnest with Stigler's (1971) paper. Peltzman (1976) analyzes a model in
which a supportmaximizing regulator allocates the benefits and costs of regulation across
groups. Becker (1983 and 1985) constructs a model in which groups exert pressure to increase
the value of their net transfers from a government, taking the outcome for any combination of
group pressure in reduced form. One exception, Goodman and Porter (1988), explicitly adds
electoral competition in a setting otherwise similar to Peltzman (1976). Other closely related
works include Rasmusen and Zupan (1991), Grossman and Helpman (1994), and Finkelshtain
and Kislev (1997). Laffont and Tirole (1990 and 1991) Dewatripont and Tirole (1995), Rajan
and Zingales (1995), and Laffont (1996) offer interesting analysis of related, but somewhat less
similar, models. While the questions I pursue differ, the technical set up of the basic model is
quite similar to that employed in the rent seeking literature. See, for instance, Tullock (1980),
Congleton (1983), Hillman and Riley (1989), Paul and Wilhite (1990), Leininger (1993), and
Linster (1993).
3 The following are examples. Im, Kaserman, and Melese (1989) find a direct link between the
regulatory expenditures of electric utilities and the approved rate base and rate of return.
Similarly, Teske (1991) finds competition is more likely to be allowed in telecommunications
markets in which government funded consumer advocacy is higher. Kaserman, Mayo, and
Pacey (1993) find that states are more likely to deregulate intrastate long distance when business
usage is more pronounced (so business users have a larger stake), and residential cross subsidies
are lower (so residential consumers have a smaller stake). Foreman (1995) finds intrastate long
distance rates are lower when consumer incomes are higher (due to the high income elasticity of
demand for longdistance services) and when large business interests are more pronounced. He
also finds that prices are higher when there are more lobbyists per legislator, reflecting easier
access for telecommunications firms.
regulated telecommunications firm may exert pressure to prevent competition while industrial
and commercial consumers (who can perhaps take advantage of preexisting trade associations to
organize their lobbying efforts), lobby to allow it. The two groups will be referred to as "the
firm" and "the consumer" for expository purposes, but the model is applicable more generally. 4
The consumer's payoff is uC if the regulator chooses his preferred outcome (the consumer
wins) and uf otherwise (u> u f). Similarly, the firm's profits are 7f if the regulator chooses its
preferred outcome (the firm wins) and 7r' otherwise (r f> c ). The consumer and the firm may
exert lobbying effort, denoted ec and ef respectively, to influence the regulatory decision.
Lobbying entails a constant unit cost of k for the consumer and kf for the firm. The magnitude
of the consumer's marginal lobbying cost may be influenced by factors such as geographic
dispersion. Legal restrictions on campaign contributions, for example, may influence the firm's
marginal cost of lobbying. The probability that the consumer's preferred outcome is selected is
taken as a function of both groups' lobbying efforts, denoted p(eC,ef).
The groups choose lobbying efforts simultaneously and noncooperatively. Each group
chooses its effort to maximize its expected payoff less lobbying costs, taking as given the other
group's lobbying effort. Formally, the consumer's problem and the firm's problem are,
respectively:
maximize w = p(ec,ef)uc +[1p(ec,ef)]uf kce, and (1)
e
maximize wF = p(ec,ef)"c +[1p(ec,ef)]zf kfef. (2)
e
4 For instance, the competition might be between two regulated firms or even two opposing
industries. In order to apply the model to nonbinary decisions, one might imagine that the
interest groups first propose and then lobby in favor of a particular policy from some feasible set.
After lobbying is concluded, the regulator would implement one policy or the other, depending
upon the lobbying activity of the groups.
The presentation focuses on the case in which a group's probability of winning is given by the
ratio of its lobbying effort to total lobbying effort, i.e.,
c
p(eC,ef ) = e (3)
ec +e
This simplification is made only for expository convenience. The results presented below hold
for any p() function and any effort cost functions that satisfy standard assumptions.5
Two features of formulation (3) are important. First, diminishing returns to effort are
present: additional effort by a group increases its probability of winning at a decreasing rate.
Second, there are diminishing returns to the "lead" in lobbying effort that one party has over its
opponent. To illustrate, suppose the consumer has exerted more lobbying effort than the firm
has. If the firm decreases its lobbying effort, increasing the consumer's lead, consumer lobbying
is less productive at the margin. Formally,
2p ec ef > c > f
S= =0 as = e (4)
f (ec + ef) <
5 Letting i= e e f and Ci(ei) represent the cost of lobbying effort, these assumptions are: 1)
> 0, 2) < 0, 3) there exists a function h(ec) with h'(ec) > 0 such that 2 0 as
ei ei.2 'ef e <
ef =h(eC), 4) Ci (e) > 0, and 5) Ci (ei) 0. Details are available upon request. Skaperdas
(1996) has shown contest success functions satisfy five reasonable axioms if and only if they
f(yi)
take the form pi (i, yj ) = f(Yi) + where pi() is the probability group i wins, yi is group
f(yi) + f(yj)
i's effort, and f() is a positive increasing function. Letting the consumer be group i and the firm
be group j and defining f(yi)=ec and f(yj)= e and assuming constant marginal lobbying costs
gives the formulation used here. Second order conditions hold globally. Contest success
functions of this form have been widely used. See, for example, Tullock (1980), Rogerson
(1982), Congleton (1983), Leninger (1993), Linster (1993), and Rajan and Zingales, 1995).
Uc f Zf c c
It is useful to define U = and = as the groups' normalized stakes. For
kc kV
the remainder of the paper, "stake" will refer to these normalized stakes and "gross stake" will
refer to the difference between a group's winning and losing payoffs. A group's reaction
function specifies its optimal lobbying effort for any level of lobbying effort supplied by the
opposing group. Ec(ef;U) and Ef(ec;H) will denote the reaction functions of the consumer and
firm respectively. It follows from equations (1)(3) that:
1
Ec(ef,U) = (efU)2 ef, and (5)
1
Ef(ec, )=(ecH)2 ec. (6)
An increase in the consumer's stake (due to changing payoffs or marginal lobbying costs)
increases its marginal return to lobbying, and so increases its lobbying effort for any given level
of firm lobbying formally  > 0 The slope of the consumer's reaction function is
influenced by the relative expenditures of the two groups. If the consumer's lobbying effort
exceeds the firm's, the consumer increases its effort to protect its lead when the firm's lobbying
increases so X > 0 If not, an increase in the firm's lobbying makes prospects dimmer for
the consumer, and he scales back his lobbying effort accordingly so X < 0 The results
for the firm are analogous.
The unique Nash equilibrium is determined by the intersection of the reaction functions. The
equilibrium values of consumer and firm effort, denoted ec*(U,H) and ef*(U,H) respectively, are
given by equations (7) and (8). The corresponding probability that the consumer's preferred
outcome is selected, p(ec*,ef*), will be denoted p*(U,H) and is given by equation (9).
HU2
ec *(U,H)= (u 2 (7)
(U + )2
ef (U, ) =u 2 (8)
p*(U, H)= (9)
u+ H
The firm's lobbying effort exceeds (falls short of) the consumer's lobbying effort and the
firm's chance of winning is more (less) than onehalf if the firm's stake is larger than the
consumer's stake. Intuitively, if the firm's stake exceeds the consumer's, the firm has a higher
incentive to lobby, leading to a higher chance of winning. Figure 1 below illustrates the two
possibilities. In the figure, the consumer's stake is held constant while the firm's stake is varied.
If the firm has relatively little at stake, say H, the equilibrium will be at a point like A where the
consumer is most likely to win. If, however, the firm's stake is relatively large, say 11, the
equilibrium will be at a point like B.
ef I Ec(efU) e =ef
Ef(e ;1)
FIGURE 11
EQUILIBRIUM
Given equations (7)(9), it is straightforward to determine the response of the equilibrium to
shifts in the groups' stakes. Increases in the consumer's stake (due to changes in payoffs or the
marginal cost of lobbying effort) shift its reaction curve to the right, increasing consumer effort.
If the firm's stake exceeds the consumer's stake, so that firm effort is higher, the firm increases its
effort to protect its lead. Otherwise the firm decreases its effort. In either case, the consumer is
more likely to win in equilibrium. The analysis of changes in the firm's stake is analogous.
Changes in institutions, such as campaign laws or the regulatory regime, or in underlying
economic conditions, such as demand or production costs, can change the stakes of both parties.
When the consumer's stake increases but the firm's stake decreases, the direct effects are for the
consumer group to lobby more and the firm to lobby less, increasing the chance that the
consumer wins. There are, however, indirect effects as well. For instance, suppose the
consumer's initial lobbying effort is higher than the firm's initial lobbying effort and the decrease
in the firm's stake is much larger than the increase in the consumer's. Then, the decrease in the
firm's lobbying could put the consumer so far ahead that he reduces his lobbying effort due to
diminishing returns. The following conditions ensure that these indirect effects do not dominate.
Condition 1. d U < 2
dU U H)
Condition 2. dU U < 2
Consumer lobbying effort increases as the consumer's stake increases if and only if Condition
1 is satisfied. Essentially, Condition 1 means that when both groups' stakes change, the change
in the consumer's stake is not trivial relative to the change in the firm's stake. Condition 2 plays
an analogous role for the firm. Table 11 summarizes the effects of changes in stakes on
equilibrium outcomes. These predictions are generally consistent with a large empirical
literature.6
TABLE 11
THE EFFECTS OF CHANGES IN STAKES7
Change in Stakes Effects of Change in Stakes
dU dfI dec* def* dp*
S+0 + ? +
0 + ? + 
S+ +a b +
+ + +a +b ?
a If and only if condition 1 holds.
b If and only if condition 2 holds.
Central Findings
I turn now to the primary findings of this research. This section develops new results
concerning the effects of important types of exogenous changes on regulatory outcomes,
lobbying effort, and the expected welfare of the groups.
The consumer group's equilibrium expected utility falls as the firm's stake increases because
the firm will exert more lobbying effort when it has more at stake. Similarly, the firm's
equilibrium expected profits fall as the consumer's stake increases. Thus, any improvement in
6 The comparative statics summarized in Table 11 essentially formalize Stigler's (1971)
argument that groups with larger economic stakes or lower costs of exerting pressure are more
likely to be the beneficiaries of regulation. For changes in the marginal cost of effort, the results
are analogous to Becker's (1983) finding that a group's relative efficiency at producing political
pressure determines how they fare politically. Hillman and Riley (1989), Leininger (1993), and
Linster (1993) show that groups lobby more and are more likely to win when the value they
place on the political prize (here, a favorable decision) increases, holding constant the other
group's valuation. Explicit consideration of the groups' utilities under unfavorable decisions is,
to my knowledge, unique to the present analysis.
7 In the table, + denotes an increase, 0 denotes no change, and denotes a decrease. The game is
qualitatively symmetric, so reversing the signs of the exogenous shocks in Table 11 reverses the
pattern of the endogenous responses.
one group's winning payoff makes the other group worse off and may reduce aggregate welfare.
This observation leads to the following proposition.
Proposition 1. "Improvements" in the efficiency of regulation or any change that increases the
gross surplus available but alters the stakes of the groups will not unambiguously improve
either group's welfare or aggregate welfare. It is possible for both groups to become worse
off simultaneously.
The intuition underlying Proposition 1 is straightforward. "Improvements" can change the
stakes of both parties and therefore alter political activity in a complex way. If the groups have
more at stake, wasteful lobbying expenditures will increase.8 Further, the probability that the
regulator's decision will favor consumers will change. This may mean that the decision with the
highest social value becomes less likely. On net, consumers and/or producers may end up worse
off, and aggregate welfare may be lower. This suggests that one should not be surprised to see
little support, or even general opposition, to changes that otherwise appear to be welfare
enhancing when the political environment is volatile; the proposed "improvements" may be more
trouble than they are worth.9
This conclusion differs from those in earlier ET models. Becker (1983) found that more
efficient taxation would be unanimously supported while more efficient subsidization would be
supported by one group but might be supported or opposed by the other. In the setting studied
8 This is related to the finding in Hillman and Riley (1989) that rent seeking activity will be less
intense when players' valuations of the political prize are less similar.
9 In a two period model in which two subunits allocate their resources between production and
power seeking, Rajan and Zingales (1995) show that the subunits may fail to agree to
contractible changes that enhance gross surplus. This occurs because the transfers that
implement "compensation" when power seeking is not of concern alter the balance of power
between the subunits. The prospect of this change in the balance of power can prevent
agreement.
here, some improvements that increase gross surplus will be supported by no one. In addition,
Peltzman (1976) and others argue that regulation insulates individual constituencies from
exogenous shocks by spreading the impact of these shocks across all constituencies. This
conclusion arises because the regulator in Peltzman's model optimally equalizes the marginal
return to allocating benefits across nonstrategic groups. While the basic insight that regulators
will tend to engage in cost and benefit spreading under certain circumstances is important, some
qualification is called for when the groups strategically alter their lobbying activity in response to
the prevailing stakes. This may be seen not only from Proposition 1 but also from Table 11.
Suppose the consumer's stake increases because his winning payoff rises. The consumer will
then lobby more intensively, increasing the probability that the decision will be in his favor and
compounding the original shock.
Table 12 presents a simple numerical illustration of Proposition 1.10 The table depicts the
following type of setting. A decision in favor of the firm (perhaps imposing regulation in a
competitive market or allowing a large sunk investment into the rate base of a utility) will cause
the price of the product it sells to rise. Before the decision is made, an exogenous increase in
service quality is imposed (or flows from a previous decision) that generates greater additional
consumer surplus if prices are low because more units are consumed, but entails a higher cost to
the firm when prices are low for the same reason. When prices are high, the improvement
stimulates demand sufficiently to increase the firm's profits, but when prices are low, the
increase in cost dominates, reducing profits. The end result is a reduction in the expected
10 In the numerical examples used in the paper, the initial parameters (uc, u, n, and 7n) and the
shocks (Auc, Auf, Anc, and Ain) are specified and everything else is calculated from equations (1),
(2), and (7)(9).
equilibrium welfare of both parties. (In Table 12, Wc denotes consumer welfare, WF denotes
firm welfare, and W=WC+WF denotes aggregate welfare.)
TABLE 12
A NUMERICAL EXAMPLE
uu u c f It u+I u+rf ec* et* p* W W' W
Initial 600 100 200 300 800 400 69 14 .83 447 203 650
Final 800 200 100 550 900 750 147 110 .57 396 183 579
A 200 100 100 250 100 350 77 96 .26 51 20 71
Entries have been rounded to the nearest integer (p is rounded to the nearest hundredth).
Marginal lobbying costs are unity for both parties.
Proposition 1 has potential implications for several current regulatory issues. For instance,
changes in policy or technology that reduce the potential cost independent power providers
(IPPs) would incur to deliver power to final consumers may make customers lobby harder for
retail competition in electricity provision." Similarly, regulated electric utilities would lobby
harder against retail competition since the competition they would face if final customers could
choose their supplier would stiffen. The end result could be reduced equilibrium expected
welfare for all parties.12 Similarly, improvements in the quality of products or services
11 Traditional electric utilities use a technology characterized by high fixed costs but very low
marginal costs until capacity is pressed. Other techniques are then used to augment base
production. Independent and competitive firms (IPPs) as well as the traditional regulated utility
can use new low fixed cost technologies to produce power above base capacity. While
customers might be expected to prefer to have the opportunity to choose their supplier (when
feasible), regulated utilities will prefer to reduce potential competition by preventing their
customers from gaining direct access to IPP power. Hunt and Shuttleworth (1996) provide a
useful discussion of the potential for competition in electricity provision.
12 By expanding the basic model (as alluded to in note 4) I explored this possibility using
numerical simulations (closed form solutions or general comparative statics are not feasible in
the expanded game structure). The additions to the model used in these simulations were: 1) a
linear demand curve, 2) constant marginal cost technologies (with a capacity constraint and fixed
cost for the base technology), and 3) additional stages in the lobbying game. In the first stage of
the expanded game the groups lobby over the adoption of retail competition. In the second stage,
if competition was not implemented, each group proposes a price for the regulated product from
the set of prices that at least cover the firm's costs. In the third stage (if needed) the groups
lobby for their proposed price. The regulator then chooses a price and payoffs are realized. In
potentially subject to universal service requirements may make regulated firms lobby harder
against universal service (to engage in cream skimming) and customers lobby harder for it.
Again, all parties might find their equilibrium expected welfare reduced.13 Finally, the use of
twopart tariffs instead of simple linear prices has been widely advocated as a potential remedy
for the deficit created by marginal cost pricing in strong natural monopolies. However, in a
political setting the firm may use the additional pricing flexibility to extract more consumer
surplus than needed to cover its fixed costs. Both parties will have more at stake when the level
of the twopart tariff is determined than when a linear price is set, resulting in higher lobbying.
While the greatly increased ability to extract surplus using twopart tariffs will tend to make the
firm better off, both consumer and aggregate equilibrium expected welfare might be reduced.14
Previous investigations have shown that individual groups gain when the efficiency with
which they exert political pressure increases.15 However, institutional changes such as
this setting, small reductions in the IPPs' realized marginal cost make both groups worse off (in
expectation) over a sizeable range of parameters. Large reductions in the IPPs' realized marginal
cost make the firm worse off but make the consumer better off because the reduced price under
competition swamps the effect of increased firm lobbying. Additional information concerning
these simulations is available upon request.
13 By expanding the game in a way similar to that discussed in note 12, it is possible to use
numerical simulations to investigate this possibility as well. Again, over a nontrivial portion of
the parameter space, everyone is worse off due to the "improvement." Additional information
concerning these simulations is available upon request.
14 See, for example, Berg and Tschirhart (1988) for a discussion of the role of twopart tariffs in
utility regulation. Numerical simulations of the impact of twopart pricing require only one
additional stage in which the two groups propose either a linear price or a twopart tariff,
depending upon the institutional structure. With a constant marginal cost, consumers are worse
off for any fixed cost (that may be covered with a linear price) and any combination of firm and
consumer lobbying costs between 1 and 50 (I did not search beyond 50). If the firm's marginal
lobbying cost is very much below the consumer's, aggregate welfare increases, if not it falls.
Additional information concerning these simulations is available upon request.
15 For instance, Tullock (1980) shows that "bias" in favor of one group makes that group better
restrictions on campaign contributions, ethics laws, or motor voter programs effect the lobbying
costs of all groups. I now extend the analysis to consider such changes.
Each group's welfare falls when its own marginal lobbying cost increases, but rises as its
opponent's marginal lobbying cost increases. The magnitude of these effects depends critically
upon the initial values of the marginal lobbying costs. The loss a group sustains when its
marginal lobbying cost increases is relatively small when its initial marginal lobbying cost is
high relative to its opponent's marginal lobbying cost for two reasons. First, the direct increase
in cost is small, as the group's initial lobbying effort is low due to the high initial marginal cost.
Second, since the group's lobbying effort is low initially, the decrease in the group's own
lobbying effort brought about by the cost increase leads the group's opponent to lobby less,
partially offsetting the negative consequences of the first effect.16 If instead the group's marginal
lobbying cost was initially small relative to its opponent's marginal lobbying cost, the first effect
would be larger and the second would reinforce rather than oppose it.
Similarly, if a group's opponent's cost is small (large) relative to the group's own cost, the
opponent's lobbying effort will be relatively high (low). Therefore, an increase in the opponent's
marginal lobbying cost induces a relatively large (small) decline in the opponent's lobbying.
This leads to Proposition 2.
off, Rogerson (1982) shows that the political advantage of an incumbent monopolist increases
their expected payoff, and Becker (1983) shows that political success depends upon the groups'
marginal productivity in the production of "influence."
16 Indirect effects through changes in a group's own lobbying drop out via the envelope theorem.
Proposition 2. Groups that are less (more) efficient at utilizing the political process gain (are
harmed) when all groups experience equal increases in the marginal cost of lobbying
effort. 17
Proposition 2 may help to explain why public efforts to increase voter participation often
generate less popular attention than efforts to reform campaign finance laws. If the general
public is less efficient at generating political pressure in support of its interests than are special
interest groups, making it harder for special interest groups to deliver pressure enhances welfare
most expediently.
The simple model developed above may also help to explain the deregulation of certain
industries. Peltzman (1989) explores the ability of the ET to explain several cases of
deregulation, focusing on the erosion of rents accruing to firms in the regulated industry. As
discussed above, the regulator in Peltzman (1976) spread shocks across all groups, so declining
rents to firms would be symptomatic of a general decline in wealth under the existing regulatory
regime. In the case of trucking, he concludes that substantial and sustainable rents were
eliminated over the opposition of their recipients. He also concludes that AT&T was still
receiving substantial regulatory rents immediately prior to divestiture. In his view then, the ET
does not readily explain trucking and longdistance telecommunications. Levine (1989) also
questions the predictive power of the ET, contending that significant rents were eliminated as a
result of airline deregulation as well.
17 In general, very weak groups benefit from across the board increases in marginal lobbying
costs while very strong groups benefit from across the board decreases in marginal lobbying
costs. The fact that the dominant effect switches where the two marginal lobbying costs are
exactly equal is an artifact of the functional form employed, particularly the assumption of
constant marginal cost.
Peltzman and Levine focus on reductions in the stake of the regulated firm. However, even
when the benefits accruing to all parties under regulation are growing, it is possible for the
difference between what those opposed to regulation would receive if regulation were abolished
and what they receive under the existing system of regulation to increase. The contribution of
this paper is to suggest that when groups lobby strategically, increases in the stakes of those
opposed to regulation may outweigh the continued interest of the firm (industry) in maintaining
regulation. My model may be applied to this question by assuming that the decision to be made
is whether to deregulate and that the parties disagree about which outcome is favored. Increases
in the stake of the group favoring deregulation make that outcome more likely, and if both
parties' stakes increase, the question is one of relative magnitudes. This gives Proposition 3.
Proposition 3. Suppose the rents accruing to all beneficiaries of regulation increase. Then
deregulation can still become more likely if the stakes of those adversely effected by
regulation increase sufficiently.
The fact that MCI's application to provide long distance service was one of the crucial steps
on the path to competition in the provision of long distance service suggests that the stakes of
potential competitors deserve consideration.18 In addition, the rapidly increasing importance of
interstate and intercommunity trade suggests that the stakes of the users and potential
competitors of airlines, trucking, and telecommunications services may have been growing
rapidly and systematically prior to deregulation. Table 13 presents some relevant data.19 The
18 See Brock (1994) for a discussion of the divestiture of AT&T.
19 Sources: Statistical Abstract of the United States (1996) No.2; Statistics of Communications
Common Carriers (1996) Table 6.5; 1977 Information Please Almanac: Atlas and Yearbook,
New York: Simon and Schuster, 1976. Air passenger miles for 1950 are estimated from a log
log regression of air passenger miles on year for the years 1939, 1941, 1944, 1953, 1960, 1970,
1973, and 1974.
first column shows telecommunications expenditures per capital for 1950, 1960, and 1970 in
1982 dollars. The second and third columns list per capital air passengermiles and truck ton
miles for the same years. All three statistics grew rapidly prior to deregulation. The data suggest
users stood to gain more from lower prices and potential competitors stood to gain more from
entry as time passed. Seen in this light, the deregulation of these industries is more
understandable.
TABLE 13
STAKES FAVORING DEREGULATION
Telecommunications
Expenditures Air Passengermiles Truck Tonmiles
Year Per Capita Per Capita Per Capita
(1982 Dollars)
1950 94 43 1135
1960 156 176 1580
1970 226 534 2009
Entries have been rounded to the nearest integer.
In the foregoing discussion, lobbying activity resulted in undesirable outcomes. Institutions
that constrain or reduce lobbying may therefore enhance social welfare. Consider the role that
profit sharing can play in this regard. Whenever the profit sharing scheme is not extremely
regressive, the transfer to the consumer is higher when the firm's profits are larger, so profit
sharing reduces the firm's stake (d7rf
larger when profits are higher, it is also natural to assume that the gain in the consumer's payoff
is largest when profits are largest, so profit sharing reduces the consumer's stake as well
(duf>duc>0 and dU<0).
Profit sharing unambiguously increases the consumer's welfare because it increases the
consumer's gross payoffs and reduces the firm's stake. The firm may also gain on balance if the
effect of the reduced consumer lobbying outweighs the direct effect of reduced gross payoffs.
The decline in lobbying activity suggests that aggregate welfare rises under profit sharing. In
order to ensure that aggregate welfare increases, it is sufficient (not necessary) that transfers are
valued at least as highly by the consumer as by the firm. This gives Proposition 4.20
Proposition 4. Profit sharing reduces the lobbying activity of both groups and increases
consumer welfare. The firm 's net profit may also increase when profit sharing is imposed.
Furthermore, aggregate welfare is unambiguously improved if the transferred funds are at
least as valuable in the hands of the consumer as in the hands of the firm.
Consider the numerical illustration of Proposition 4 summarized Table 14. In the example,
profit sharing entails a transfer of 50% of the firm's realized profits to the consumer. The
imposition of profit sharing reduces lobbying substantially and leads to gains for all parties.
TABLE 14
A NUMERICAL EXAMPLE
uC ut c I n ec Ie p IW2c W"'[ W
Initial 800 400 20 800 90 175 .34 446 361 807
Final 810 800 10 400 .24 9.5 .03 800 381 1181
A 10 400 10 400 89 165 .31 354 20 374
Entries have been rounded to the nearest integer (p is rounded to the nearest hundredth).
Marginal lobbying costs are unity for both parties.
Sappington and Weisman (1996) report that as part of the initial movement toward incentive
regulation in the telecommunications industry, fourteen states and the District of Columbia had
instituted earnings sharing plans as their primary form of regulation as of 1995. In addition to
improved incentives for efficient operation, this analysis suggests these plans have desirable
political properties that may have contributed to their popularity. This is particularly true if the
20 Weisman (1994) argues that firms have an incentive to build profit sharing into their suggested
regulatory plans rather than asking for pure price caps. This is because the regulator may decide
she would actually like a lower price after instituting the plan, and therefore might allow
competitive entry. Profit sharing dilutes the regulator's incentive to engage in such practices by
partially aligning the interests of the regulator, consumers, and the firm.
uncertainty associated with the initial stages of a shifting regulatory climate led to a heightened
potential for political conflict.21
Conclusion
The version of the Economic Theory of Regulation developed here leads to several new
results. In particular: 1) changes in policy or technology that increase the potential gross surplus
in regulated markets can reduce welfare, 2) the group whose marginal lobbying cost is higher
(lower) benefits (is harmed) when all groups experience equal increases in their marginal
lobbying costs, 3) a more consistent explanation of deregulation is possible when changes in the
stakes of those opposed to regulation are considered in addition to changes in the rents accruing
to the regulated industry, and 4) profit sharing reduces lobbying activity, improves consumer and
aggregate welfare, and may even increase the firm's welfare.
These conclusions hold more generally, provided the basic structure of the model is not
altered. Several other extensions merit investigation. A complete theory of the outcome
function is needed to permit a fully general analysis of nonbinary decisions and alternative
institutional designs. Allowing more groups may prove to be important. To see why, notice that
with linear and nondiscriminatory pricing, the interests of all consumers are aligned; they all
want a lower price. With nonlinear pricing or third degree price discrimination, this link is
21 The states were: Alabama, California, Colorado, Florida, Georgia, Louisiana, Maryland,
Minnesota, Mississippi, New Jersey, New York, Rhode Island, Tennessee, and Texas. Currently,
most states have moved toward regulatory plans that more closely resemble pure price caps. The
fact that earnings sharing reduces the power of the incentive plan in addition to reducing
lobbying effort is a drawback to the application of Proposition 4 here. In Chapter 3 I empirically
investigate regulatory plan choice. Using several variables selected to represent both the need
for better incentives and the political environment, I find that higher political costs result in a
higher likelihood of earnings sharing.
destroyed, probably allowing politically strong consumers and the firm to benefit at the expense
of politically weak consumers.22 The incorporation of informational asymmetries might also
yield important insights.
22 Beard and Thompson (1996) make a similar point in a different type of model.
CHAPTER 3
DETERMINING THE RULES OF THE GAME:
REGULATORY REGIME ADOPTION IN THE U.S.
TELECOMMUNICATIONS INDUSTRY
Introduction
Rapid change has become commonplace in the telecommunications industry. Evolving
technologies and products made interstate long distance competition feasible, leading to the
divestiture of the Bell System on January 1, 1984. Similarly, the development of wireless and
other modem technologies has continually reduced the spectrum of operations that might
reasonably be regarded as natural monopolies. One interesting facet of the evolution of the
telecommunications industry since divestiture is the use by many states of nontraditional regimes
to regulate the intrastate operations of telecommunications firms. The first alternative regimes to
appear were simple rate case moratoria where prices were simply frozen for a specified (usually
short) period of time. Next, more sophisticated plans known as earnings sharing regulation
(ESR) that called for some sharing of earnings between the firm and consumers began to appear
and eventually became widespread. Finally, fairly sophisticated forms of price cap regulation
(PCR) with rules determining future price reductions (Xfactors) and specified procedures for
deciding how to handle extreme contingencies beyond the firm's control (Zfactors) appeared.
By 1996, more states used some form of PCR to regulate their dominant telecommunications
firms than any other type of plan.1 In this paper, I develop a simple theoretical model of
1 The classification of regulatory plans was derived from information reported in BellSouth
Telecommunications (19871995), and State Telephone Regulation Report (19941997).
regulatory regime adoption and use it to inform an empirical investigation of regulatory patterns
in the U.S. telecommunications industry. I find that regime adoption patterns can be explained
fairly well using the basic theoretical differences in the incentive properties of regulatory
alternatives and a simple theory of the political economy of regulation.
Exploring the reasons that states implement different types of plans to regulate intrastate
telecommunications is an important task for several reasons. Understanding why states have
done as they have up to this point may help to predict their future actions. For example,
assuming competition continues to develop, what might future patterns of deregulation look like?
Determining whether the observed pattern of regime change has been simply a prelude to
deregulation or embodies deeper intrinsic characteristics might produce lessons that apply to
regulation of in other industries, for example electricity. Further, the study of regulatory regime
adoption patterns in the telecommunications industry provides fertile ground for exploring
various strands of economic theory outside the realm of public utility regulation, particularly
within the area of constitutional political economy. For instance, how are the rules of the game
shaped by the political and economic concerns of the polity to be governed by those rules?
A great deal of attention has been given to the theoretical properties of traditional rate of
return regulation and alternative regulatory structures.2 In addition, several empirical studies
have focused on the effect of regulatory structure on the performance of telecommunications
firms.3 Donald and Sappington (1995 and 1997) investigate the empirical determinants of state
2 A few examples are Averch and Johnson (1962), Bailey (1978), Lewis and Sappington (1989),
Schmalensee (1989), and Brown et al. (1991). Sappington and Weisman (1996) provide a
comprehensive and nontechnical overview of the role of regulation in the modern
telecommunications industry.
3 See Kridel, Sappington, and Weisman (1996) for a comprehensive survey of the empirical
literature on the effects of incentive regulation on performance in the telecommunications
decisions regarding the implementation of alternative regulatory regimes in the
telecommunications industry.4
This paper builds on the work of Donald and Sappington (1995 and 1997) in several
important respects. First, they classify all regulatory plans as either rate of return or incentive
regulation. However, important differences exist between ESR and PCR, the two major
alternatives to traditional rate of return regulation. I separate ESR and PCR. I find that doing so
produces important new insights. Second, and due in part to the difference in plan classification,
I model regime selection differently. Specifically, I account more explicitly for political factors,
the role of uncertainty, and the potential for unplanned for contingencies.
The following are among my key findings. First, higher costs of making the transition to an
alternative regime (as reflected empirically by cumulative experience with alternative regimes,
regulatory budgets, union strength, and party control) or more uncertainty (as reflected by lower
regulatory budgets or more frequent rate filings historically) make adopting an alternative regime
less likely. Second, higher perceived benefits from improving incentives for efficient operation,
(as reflected by larger markets or higher labor costs) lead to a higher likelihood that an
alternative to traditional rate of return regulation (RORR) will be adopted. Third ESR is more
likely relative to PCR when more rate cases were filed in the past (reflecting a greater incidence
of unforeseen contingencies) or when there are more registered lobbyists per legislator
(reflecting more groups competing for influence and placing demands on the time of regulators
industry. Berg and Foreman (1996) provide a compact appraisal of this literature.
4 Classifying all plans other than rate of return regulation as "incentive regulation," as in Donald
and Sappington (1995 and 1997), Zhuang (1997) uses an ordered probit model to examine the
timing of the adoption of incentive regulation. There is a large empirical literature concerning
the determinants of other regulatory outcomes. See, for example, Primeaux et al. (1984), Nowell
and Tschirhart (1990), Teske (1991), Kaserman, et al. (1993), and Foreman (1995).
and the firm). This may reflect the theoretical ability of ESR to economize on hearings due to
unforeseen contingencies (Zfactors) and reduce the adverse effects of uncertainty relative to
PCR.
The remainder of the paper is organized in the following manner. Section 2 develops a
theoretical model to guide the empirical analysis of regime selection. Section 3 formulates the
empirical model and tests the theory set out in section 2. Section 4 concludes and considers
possible avenues for future research.
A Simple Model of Regulatory Regime Adoption
Regulatory regime adoption is affected by a wide variety of economic and political factors.
The perceived efficiency gains from switching to a new form of regulation, as well as the
perceived cost of making the transition to a new regime, are important economic considerations.
Since the efficiency gains may flow largely from cost reducing effort that is hard to observe and
quantify, moral hazard must also be considered.5 Since alternative plans may not affect all
groups symmetrically, the relative political strength of the regulated firm and consumers is also
important. No regulatory plan provides fully for all possible contingencies. When contingencies
that have not been planned for arise, their impact may differ depending upon which regime is in
effect. Therefore, the possibility that unplannedfor contingencies may arise and the cost of
dealing with these contingencies may be a factor in regime adoption. In this section, I construct
a simple formal model of regime adoption that encompasses each of these factors. The
5 Moral hazard exists when the principal can not observe whether or not an agent has taken the
desired action. Therefore, contracts between the principal and the agent must be based upon
indirect indicators of the agent's action.
comparative statics derived from this model provide hypotheses that are tested in the empirical
work that follows.
I assume that the demand for the regulated firm's product is perfectly inelastic as long as the
total charges expected by any customer are below that customer's reservation value (R). This is
a reasonable approximation for local telephone service.6 It may also be a reasonable
approximation where twopart pricing is used and income effects are negligible, in which case R
is consumer surplus gross of the fixed charge. For simplicity, I normalize the number of
consumers to one. Allowing an arbitrary number of different consumers would make no
difference to the model as long as the consumer with the lowest reservation value chose to
consume the service in question. I can describe a variety of regulatory regimes with three
parameters: price, p, target earnings, E, and the percent of observed earnings above or below the
target to be retained by the firm, ca.
RORR obtains if a = 0. Under a stylized interpretation of RORR, the level of allowable
earnings (revenue less measured costs) for some period is determined in regulatory proceedings
at the beginning of the period. Prices are then set to achieve the desired level of revenue. If
earnings differ from the target, some mechanism is employed to eliminate the discrepancy. For
example, this may take the form of a refund to consumers or lower prices in the next period if
earnings exceed authorized levels. Since the firm is guaranteed a predetermined level of
earnings regardless of its cost, it has no incentive to devote unmeasured effort to reduce costs.
For example, the time that management spends motivating employees and streamlining
6 Several empirical studies have found the elasticity of demand for basic local telephone service
to be near zero. See, for example, Taylor (1993).
production (as well as the intensity with which these endeavors are undertaken) is not easily
observed and therefore may not be appropriately rewarded under RORR.7
Recently, alternative regulatory plans, intended to provide better incentives than RORR, have
become popular in the telecommunications industry. For my purposes these alternative regimes
can be grouped into two categories: earnings sharing regulation (ESR) and price cap regulation
(PCR). ESR mitigates the incentive problems associated with RORR by allowing the firm to
keep some fraction of its earnings. Values of ca between 0 and 1 correspond to ESR. I assume
that values of ca for ESR regimes are chosen from the interval [ca, U] with a > 0 and a < 1.
This reflects the fact that in RORR, ESR, and PCR are three distinct regulatory forms.
Additional reasons for these bounds are taken up in note 15 below. In practice, ESR regimes
have typically involved a split of observed earnings along the lines of 50/50, 60/40, or 70/30.
ESR induces the firm to increase cost reducing effort, but not to provide the optimal amount
since it still does not capture all of the marginal benefits of its effort. Under PCR, prices are set
at the beginning of the relevant period and the firm is allowed to keep any earnings it can
generate at those prices. Thus a = 1 corresponds to PCR. The firm captures all of the gains
from cost reducing effort under PCR, so the optimal provision of cost reducing effort may be
induced.8
7 For simplicity I treat RORR as simple cost of service regulation. In doing so I abstract from
several institutional details, such as regulatory lag.
8 When the firm's performance is used to set future price caps, or when the firm is allowed to
petition for rate relief if earnings turn out to be below a certain level, the ability of the price cap
plan to induce effort is obviously reduced. Therefore, the difference in incentives between a
price cap plan and traditional rate of return regulation with regulatory lag may, in actuality, be
less drastic.
The firm may exert effort, e, to reduce the cost of providing the regulated service. The
2
disutility of effort is given by V(e) = The cost of the regulated service that is observed ex
post by the regulator is C(e) = c be where b is the marginal benefit of cost reducing effort. It
is common knowledge that both c and b are distributed uniformly on the intervals [c, c] and
[0, b], respectively. The assumption that c has mean zero is not important since any nonzero
mean can simply be subtracted from the reservation value up front.9 Neither the firm nor the
regulator know the exact realization of b or c ex ante. The firm optimally sets the marginal cost
of effort equal to its expected marginal benefit. The firm bears a fraction of observed cost equal
b
to ca and the expected marginal benefit of effort is . Therefore, the firm's choice of effort
2
under different regulatory regimes and expected benefit levels, e(c, b), is given by
b
e(c, b) = a. Under PCR the firm provides the level of effort that maximizes the net benefit
2
9 The functional forms used throughout this paper are chosen only to ease the presentation. All
of the results hold much more generally. Any convex disutility of effort function may be used.
The cost function may be easily generalized as follows. Define cost as C and let C = c B
where B is cost reduction due to effort. Let B be distributed on the interval [0, B(e, b)] according
to the density function g(B,e,b) where e is effort and b is a parameter reflecting the marginal
productivity of effort. Defining B(e, b) to be the expected benefit of effort given a particular
effort level and productivity parameter, it is sufficient to make the standard assumptions that
B(e,b)is concave in e, B(0,b)= 0, Bb 0, and eb > 0.
Let c be distributed on the interval [c(b, a), c(b, C)] according to the density function f(b,G)
with mean c(b) where a7 is a noise parameter that effects the variance and the bounds of c, but
not the mean. Changes in the potential benefits from cost reducing effort may shift both the
mean and the bounds of the distribution of c. For instance, higher labor costs lead to higher
mean cost, a higher upper bound on cost, and more opportunities for cost savings from allocating
labor efficiently. It is useful to impose the restriction that cb = 0. That is changes in the
potential benefits of effort do not substantially effect the difference between the upper bound on
cost and the mean cost corresponding to a zero effort level.
from cost reduction activity while under RORR the firm exerts no effort. It may be useful to
interpret e = 0 as the minimal level of managerial effort necessary to keep the firm functioning,
so that e measures increments of effort above this minimal level.
The firm's earnings, E, are given by:
E= a(pC(e)E)+E (1)
where p C(e) E gives the firm's earnings beyond the target level. Rearranging gives:
E = p + (1a C(e). (1')
It is evident that an indeterminacy between p and E will arise under ESR because of the simple
regulatory structure I utilize. This is resolved by letting x represent the net payment to the firm,
excluding cost sharing (x = up + (1 ca)E). Under RORR, x = E, under PCR x = p, and under
ESR, many combinations of p and E correspond to any particular value of x.
One might expect the state to adopt a price cap plan to yield the highest possible surplus and
then to set prices in accord with the relative political strength of the firm and consumers.
However, other constraints on the regulatory system may alter this intuition. In particular, it is
usually incumbent upon the regulatory body to ensure the financial viability of the firm. Indeed,
poor financial health for the firm can harm consumers, since supply disruptions or quality
deterioration may arise. Ensuring that the firm is viable even when realized costs are high may
require high prices. In such a setting consumers will be better off under earnings sharing even
though some efficiency is sacrificed because prices can be set high enough to keep the firm
whole while consumers get some relief ex post for low cost realizations.10
10 See Schmalensee (1989) for an in depth discussion and numerical simulations of this point.
To capture this phenomenon I assume that the chosen regulatory regime must satisfy a
limited loss constraint that earnings be nonnegative for even the highest cost outcomes. That is,
a regime under which the firm would go bankrupt if the random component of its operating cost
turns out to be very high may not be instituted. The limited loss constraint does not apply to the
type of rare events that might be classified as Zfactors, such as natural disasters or extreme
economic downturns. Since the effects of such rare events can be observed and separated from
the day to day operations of the firm, they may be adjusted for ex post as described below.
However, in order for alternative forms of regulation to have better incentive properties than
traditional regulation, the regulator must commit not to adjust the firm's earnings ex post beyond
agreed to sharing and corrections for Zfactors, thus the need for the limited loss constraint.
Given the notation above, the limited loss constraint (LL) becomes
x ac > 0. (LL)
The regulator incurs transition costs when moving from RORR to either ESR or PCR. These
transition costs may flow from the activities associated with formulating and implementing a
new plan such as gathering and disseminating information or retraining personnel. They may
also flow from the need to overcome institutional inertia. For convenience, I assume that all
transition costs are netted out of consumer surplus. Transition costs are represented by T(c)
with T(c) = 0 if RORR is implemented, T(c) = TESR if ESR is implemented, and T(1) = TpcR if
PCR is implemented." Allowing both the regulator and the firm to incur transition costs in no
way alters the results presented below.
11 In actuality, some transition costs may be intangible costs imposed on regulatory personnel.
Allowing two types of transitions costs formally, however, only makes the notation more
complex. I do not explicitly consider the possibility of moving from ESR or PCR back to RORR
or of moving between ESR and PCR. It is rare for a state to switch from ESR or PCR to RORR,
so there is not enough data to check predictions about such changes. It has been fairly common
A thorough explanation of state regulatory regime adoption patterns requires a theory of
political economy. One such theory is what has become known as the Economic Theory of
Regulation.12 According to this theory, regulatory institutions allocate economic benefits in an
effort to maximize their own objectives, usually interpreted as "political support." For example,
elected regulators may be interested in garnering votes directly or campaign contributions that
indirectly yield votes (as are those who appoint nonelected regulators). Similarly, appointed
regulators might wish to secure favorable opportunities for future employment or to enhance
their reputation in the community by securing charitable "civic" contributions. On the other side
of the political market, the interest groups affected by regulatory decisions offer political support
to the regulatory body (or engage in lobbying activities) in an effort to secure a higher level of
economic benefits for themselves.
I model this process in the following way. As is common in the normative regulatory
economics literature, I assume the regulator's preferences depend upon a weighted sum of
consumer surplus (CS) and profit (rt). The relative weights placed on consumer surplus, 0, and
profit, 10, may be interpreted to reflect the relative political influence of consumers and the
firm. The regulator also values direct political support, L. L may represent, for instance, efforts
to generate votes, campaign contributions, promises of future employment, or civic programs.
One unit of political support is defined as the amount of direct political effort on the part of the
for states to move from ESR to PCR, but predictions regarding the choice between ESR and PCR
follow readily from the simpler model presented here.
12 The ET began in earnest with Stigler's (1971) paper. Peltzman (1976) and Becker (1983)
provided early formal models. For further theoretical work, see Goodman and Porter (1988),
Grossman and Helpman (1994), and Finkelshtain and Kislev (1997). Laffont and Tirole (1991)
and Laffont (1996) study the role of interest groups in regulation under asymmetric information
and a very simple political structure.
1
firm required to make the regulator willing to forgo units of consumer surplus. The
0
1
regulators' utility function is then given by Ur = OCS + (1 0)7r + L. I assume 1 0 > , so in
2
the absence of at least some direct political support from the firm, the regulator would favor
consumer surplus over profit.
The firm may offer direct political support of L to the regulator at cost K(L) = L 13 The
2
marginal cost of generating one unit of direct political support is assumed to be increasing in the
amount of political support generated. This reflects the fact that the firm's ability to engage in
such endeavors is constrained by many legal and social factors. For instance, outright bribery is
illegal, states place limits on campaign contributions, and there are a limited number of jobs that
may reasonably be offered to ex regulatory personnel.
Regulatory regimes must often deal with issues outside the scope of their original provisions.
To capture the effects of such contingencies, I assume that there is some probability, 0, that a
rare event occurs. The rare event causes a random and observable surplus of S to accrue to the
firm. Any particular realization of S is drawn from the uniform distribution on [S, S].14 Under
RORR, it may or may not be necessary to hold additional hearings in order to decide what to do
about the rare event. This is because, under RORR, the parties have already agreed to remove
any random fluctuations from the firm's earnings, and so further negotiations in that regard are
13 Allowing the lobbying term, L, to enter the regulator's utility though a concave subutility
function, Y(L), changes nothing. Similarly, any convex lobbying cost function, K(L) may be
used. The functional forms in the text are chosen only to ease the exposition. Of course, either
Y(L) must be strictly concave or K(L) must be strictly convex to guarantee the existence of a
unique interior maximum.
14 Again, this functional form is assumed only to ease the presentation. The results hold for any
not necessary. However, it may be necessary to hold additional hearings to determine the
magnitude of the rare event for ratemaking purposes. For instance, there may be a need to
physically gather information or to provide sufficient documentation to protect against possible
legal actions. I use 8 to denote the probability that an additional hearing will need to be held
regarding a rare event under RORR, conditional upon a rare event occurring. For simplicity, I
assume 8 is independent of S, S, and 4. Therefore, under RORR the probability that an
additional hearing, beyond those normally associated with running the regulatory regime, will be
needed is 08. If additional hearings are necessary, they impose additional expenses on the
regulator and the firm. I assume that the regulator's share of these costs is netted out of
consumer surplus while the firm's share is taken from the profit it would otherwise receive.
While the firm may be entitled to reimbursement for direct costs imposed by regulatory hearings,
the full opportunity cost of the managerial time spent preparing for such hearings is not likely to
be reimbursed. Thus, the share of the regulatory costs borne by the firm is not likely to be zero.
I denote the reductions in consumer surplus and profit due to hearings by kcs and kV,
respectively.
Under ESR or PCR such rare events are often referred to as Zfactors. Since ESR
agreements call for sharing according to a specified algebraic rule and PCR plans call for no
sharing, emergency hearings will be needed any time the effects of a rare event are to be
removed from the firm's earnings. However, under ESR and PCR rare events may not always
lead to emergency hearings. Instead, the regulator or the firm may request emergency hearings
to remove the effect of the Zfactor from the firm's earnings since it was entirely beyond the
firm's control. Formal hearings regarding rare events will only be held when one party finds its
distribution on any finite interval [S, S].
gain from removing the effect of the rare event from the firm's earnings to be greater than their
share of the cost of the hearings.
Zr(u) will denote the regulator's expected payoff from the possibility that a rare event may
occur. Under RORR,
Zr (0)= 0(0kcs +(1 0)k"). (2)
The regulator receives disutility from the costs to consumers, kcs, multiplied by the weight
placed on consumer surplus in the regulator's objective function, 0. She also receives disutility
from the costs imposed on the firm, kV, weighted by (1 0). These potential costs are weighted
by the probability that hearings will be held, 58.
Under ESR and PCR, if formal hearings are not held the firm keeps aS and consumers
receive (1 a)S of the surplus generated by the rare event. If hearings are held, consumers
receive the entire surplus and each party incurs costs due to the hearing. The regulator will
convene hearings and receive a payoff of O(S kcs ) (1 0)k' whenever
(s kcs)(1 0)k > 0(1 )S+(1 0)S. Similarly, the firm will convene hearings
whenever k > aS .15 Thus, for ax > a (including a = 1), it follows that:
15 In this note I discuss the upper and lower bounds on sharing parameters associated with ESR.
The upper bound is useful because the transition costs associated with moving from RORR to
ESR and from RORR to PCR may be very different. If a = .9999 were feasible and the
transition costs associated with ESR were slightly less than those associated with PCR, PCR
would never be selected. This problem could be avoided by allowing T(c) to be a continuous
weakly monotonic function with that reaches a (possibly nonunique) maximum on the interior
of the interval [0,1]. This, however, complicates the analysis without yielding any further
insight. To see the role of the lower bound, recall that the regulator convenes hearings whenever
(s kcs) (1 0)k1 > 0(1 c)S + (1 0)cS. Thus, if x < (kcs+ there would be
S(201)
some range of earnings sharing parameters where hearings would never be held. While allowing
this possibility this does not change the results or add greater insight, it complicates the
Zr 2(kcs +k (Okcs +(1 )k7) (3)
(2 01)4 S
The timing in the model is as follows. First, the regulator chooses between RORR, ESR, and
PCR, and specifies the value of the sharing parameter if ESR is chosen.16 The regulator will
choose the regime that provides her with the highest expected utility, anticipating future actions.
Next, the firm offers an amount of political support, L, conditional upon the level of expected
profit that will be determined by the regulator's decision regarding the particular level of x.17
Once the regime has begun, the firm exerts cost reducing effort, and then engages in production.
Nature determines if a rare event occurs, and hearings regarding the rare event are held if needed.
After all costs are realized and the disposition of the surplus from any rare event is settled, ex
post transfers are implemented according to existing agreements. Figure 1 below illustrates the
timing in the model.
presentation considerably. Therefore, I assume that the lower bound is large enough to rule this
out under ESR.
16 In reality, the regulator can not unilaterally institute ESR or PCR because regulated firms are
typically entitled to RORR unless they agree to another alternative. To simplify the presentation,
I abstract from this point, in effect assuming that the firm is always at least as well off under ESR
or PCR as under RORR. If a constraint is imposed upon the regulator's decisions that she can
not make the firm worse off than they would be under RORR, none of the qualitative results
change. The exposition becomes slightly more complex because over some portion of the
parameter space the limited loss constraint will bind while over another portion this new
constraint would bind.
17 In this sense, the model is similar to that in Grossman and Helpman (1994) and Finkelshtain
and Kislev (1997). All of the qualitative results used to inform the empirical analysis continue to
hold if all of the bargaining power is given to the firm by letting the offer of support be
contingent upon the type of regime, or if it is all given to the regulator by allowing them to
demand a certain level of support in return for a particular level of profit.
Firm Cost
offers reducing
conditional effort Nature Costs
support exerted determines S realized
Regulator Regulator Production Hearings Expost Time
chooses ca chooses x regarding S transfers
FIGURE 1
TIMING
Once the type of regime has been chosen and the firm has offered conditional political
support, the regulator must choose the level of x. At worst, the regulator can decline the firm's
offer and choose to maximize consumer surplus subject to the limited loss constraint (recall that
1
0 > I). Since consumers dislike higher prices, the limited loss constraint binds and the regulator
2
chooses x = ac. Anticipating this, when the firm makes its offer of political support, it can
induce the regulator to choose any level of x by providing just enough political support to keep
the regulator indifferent between the firm's proposed x and the minimum x that satisfies the
limited loss constraint. Accordingly, the following represents the firm's problem (FP).
2
Maximize x  (FP)
x,L 2
s.t. L (20 1)P ac) > 0 (RIR)
Since x and L do not affect future effort provision or the treatment of potential rare events, the
firm simply wants to maximize its earnings gross of operating costs less its expenditures on
political support. The constraint is an individual rationality constraint on the regulator's utility
(RIR). It simply indicates that the firm must supply enough political support to compensate the
regulator for the effect of increased charges to consumers. Solving the firm's problem yields the
following equilibrium value of x, denoted x* (c; c, 0):
x* (; c, 0)= ac+ 1 (4)
For the following empirical analysis, it is useful to note that equation 3 implies that under
RORR the target level of the firm's earnings will be:
x* (0;c, 0)= 1 (5)
2201)
At the first stage, the regulator will choose the regime that provides her with the highest
expected utility, anticipating the way in which future stages will play out. For any particular
value of the sharing parameter, the regulator's utility is given by:
Ur()= R (20 1)+ 0(1 )c +(1)a2c2 T() +Zr(c). (6)
4 8
The first term is simply the reservation value multiplied by the utility weight. The second is
the net disutility of the minimum price level that satisfies the limited loss constraint. The third
and fourth terms are the net utility from the benefits of cost reduction flowing to consumers and
the firm, respectively. The fifth term gives the disutility incurred due to transition costs and the
final term is the regulator's expected payoff from the possibility of rare events. The firm's
lobbying does not enter the regulator's expected utility because the firm's lobbying is just high
enough to compensate for the effects of increasing prices above the minimum level. The
envelope theorem implies that it is not necessary to solve for the optimum value of the sharing
parameter under ESR to compare the regulator's expected utility under ESR to her expected
utility under other regimes. Constructing the differences between the regulator's maximized
expected payoff under ESR and RORR, PCR and RORR, and PCR and ESR and then
differentiating with respect to the exogenous variables yields the comparative statics results
discussed below. Since the results follow from straightforward differentiation of equation 6,
formal derivations are omitted.
Observation 1. An increase in the transition costs associated / i/h an alternative,
TESR or TPCR, makes that alternative less attractive relative to both of the other
alternatives.
Observation 1 is sufficiently straightforward that no additional discussion seems warranted.
Observation 2. Increases in uncertainty, c, make PCR less attractive relative to both
ESR and RORR and make ESR less attractive relative to RORR.
Increases inc indicate more uncertainty about production costs. Since profit sharing guards
against the adverse effects of such uncertainty, ESR becomes more attractive relative to PCR
when there is more uncertainty.1 Since the RORR weakens the limited loss constraint to the
greatest degree, both PCR and RORR become less likely relative to RORR when there is more
uncertainty.
Observation 3. Increases in the expected benefit of cost reducing effort, b, make both
ESR and PCR more attractive relative to RORR.
Under RORR, no cost reducing effort is provided, so both ESR and PCR become more
attractive relative to RORR when the expected benefit of cost reducing effort is higher. The
effect of an increase in the marginal productivity of effort on the choice between ESR and PCR
depends on the relative political importance of consumers and the firm. More cost reducing
effort is provided under PCR than under ESR, but consumers receive a share of profits under
ESR if costs turn out to be very low. Therefore, increases in the expected benefits of cost
18 See Schmalensee (1989) for an in depth discussion of this point.
reducing effort make PRC more (less) attractive relative to ESR if the regulator places a large
(small) weight on profit relative to consumer surplus.
Observation 4. PCR is less attractive relative to ESR when the probability of a rare
event, 4, or the costs associated i ith regulatory hearings, kcs and k", are higher.
Under ESR, some of the effects of rare events on the firm's earnings are automatically
removed by the sharing rule. Therefore, the chance that neither the firm nor the regulator will
wish to initiate hearings is higher under ESR than under PCR. Thus, ESR economizes on the
expense of hearings associated with rare events relative to PCR, making ESR more attractive
relative to PCR when rare events are more likely or regulatory proceedings are more expensive.
Since there is some chance (18) that hearings will not be needed under RORR when a rare event
occurs, increases in the probability of a rare event or the cost of regulatory proceedings have an
ambiguous impact on the attractiveness of RORR relative to both ESR and PCR.19
Observation 5. Both ESR and PCR become more attractive relative to RORR when
the probability that additional hearings will be needed under RORR when a rare
event occurs, 8, is higher.
Under ESR and PCR, there is some chance that neither the firm nor the regulator will wish to
convene additional hearings when a rare event occurs. The potential savings occasioned by this
possibility increase when hearings are more likely to be needed under RORR when a rare event
occurs, increasing the attractiveness of ESR and PCR relative to RORR.
19 Similarly Chapter 2 showed that institutionalized profit sharing arrangements reduce
strategic lobbying activity, lowering political costs, and Weisman (1994) shows earnings sharing
can smooth relations between the regulator and the firm regarding competitive entry by partially
aligning the interests of the firm and consumers.
The political importance of the firm and consumers also affects regime adoption. However,
inspection of equation 6 reveals that whether an increase in the weight the regulator attaches to
consumer surplus or profit will increase or decrease the likelihood of a particular alternative
depends upon the values of the other variables in the regulator's maximized utility function. For
instance, when the regulator places more weight on consumer surplus she will incur more
disutility from the increases in x needed to satisfy the limited loss constraint under ESR relative
to RORR, but will receive more utility from the expected efficiency gains to be shared with
consumers as well.
The Empirical Model
The dependent variable, PLANt, takes on the values 0, 1, or 2 if state i employed RORR,
ESR, or PCR as its primary form of regulation of intrastate telecommunications in year t.20
Following the divestiture of the Bell System on January 1, 1984, each state continued to operate
under RORR. In 1986, Georgia, Missouri, New York, and South Dakota instituted temporary
moratoria on rate proceedings. In the late 1980s such short term rate freezes were a popular
temporary solution among states looking for an alternative to traditional forms of regulation. As
ideas developed and experience increased, many of these states moved to ESR. Gradually states
adopted PCR until it became the dominant regulatory form in 1996. Table 1 shows the total
number of each type of plan in effect in each year from 1986 to 1997.
20 The classification of regulatory plans was derived from information reported in BellSouth
Telecommunications (19871995), and State Telephone Regulation Report (19941997) Some
states use different plans for companies of different sizes (when there are multiple companies
within the state). In such cases, the plan prescribed for the Regional Bell Operating Company
(RBOC) in the state is used as the RBOCs are the dominate intrastate telecommunications firms
and this procedure makes the choice most comparable across states.
TABLE 21
REGULATORY REGIME PREVALENCE IN THE UNITED STATES: 19861997
Regime 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Traditional 47 37 36 30 24 20 19 17 20 18 14 12
Rate Freeze 4 10 11 10 9 8 6 5 2 2 4 4
Earnings Sharing 0 3 3 8 14 19 20 23 20 18 4 4
Price Cap 0 0 0 0 1 1 3 3 6 10 27 29
Deregulation 0 1 1 3 3 3 3 3 3 3 2 2
My sample includes regulatory plans in effect from 1991 through 1997. By the early 1990s,
the number of states operating under rate case moratoria had fallen and most of those that were
in effect were long term plans, not stop gap measures, and long term rate case moratoria are
essentially simple versions of PCR. Therefore, to simplify the empirical modeling, I count rate
case moratoria adopted after 1990 as price cap plans.21
My sample includes 45 of the 50 states. Alaska, Hawaii, Idaho, Nebraska, and South Dakota
are excluded from the analysis. Alaska and Hawaii are excluded because their unique
circumstances may make them incompatible with the rest of the sample. For instance, no
Regional Bell Operating Company (RBOC) maintains a presence in those states. Nebraska
adopted near total deregulation of its telecommunications industry in 1987 and Idaho and South
Dakota adopted very extensive deregulation in 1989.22 These three states are excluded because
three observations are not enough to form a separate category for analysis.
States do not reevaluate their regulatory regimes every year. In fact, most nonRORR plans
are scheduled to last for several years when they go into effect. Thus, while there are 315 total
state plan years from 1991 to 1997, the number of real decisions regarding plan adoption is much
lower. Therefore, only the observations for which the plan in effect was in its first scheduled
21 Starting the sample in 1992 instead of 1991 or dropping the states with rate case moratoria
does not qualitatively alter the results presented below.
22 Including these states as price cap plans does qualitatively alter the result presented below.
year are included, reducing the number of observations to 209. This recognizes that states
committed to a plan for multiple years do not have the same latitude to make decisions that other
states do.23
I employ the multinomial logit model to analyze the observed pattern of regulatory regime
adoption across states.24 Under the multinomial logit model, the probability that state i operates
under alternative in year t is given by
exp('x,,) (7)
P(PLANt = j) = 2 (7)
exp(p3x,,)
1=0
where xt is the vector of explanatory variables for state i in year t and 3,, /= 0,1,2, are vectors of
parameters to be estimated. It is conventional to set P3o equal to 0 as a normalization. This gives:
exp(p'xt)
P(PLANt = j) = 2xp (8)
1 + Y exp(p'x3t)
1=1
I estimate the model by maximum likelihood.
23 Again, including all plans does not qualitatively alter the results presented below. Also, a few
states switched from ESR back to RORR during the period in which ESR was scheduled to
remain in effect. I count these states as RORR states during the year they switch if they operate
under RORR for more than half of that year. Otherwise, I count them as RORR beginning the
next year. Waiting until the next full year to change the classification of these few observations
does not alter the results.
Perhaps the best way to model plan adoption would be to include every observed plan along
with four dummy variables to capture the following five possibilities: 1) previous commitment to
ESR, 2) previous commitment to PCR, 3) no previous commitment and operation under ESR in
the previous year, 4) no previous commitment and operation under PCR in the previous year, or
5) no previous commitment and operation under RORR in the previous year. Unfortunately,
these dummy variables can not be supported by the data. It was exceedingly rare for a state pre
committed to earnings sharing to not operate under earnings sharing and all states previously
committed to price caps operated under price caps. Similarly, while a number of earnings
sharing states switched to price caps, only a few earnings sharing states switched back to rate of
return plans, and no state switched from a true price cap plan to any other plan. Thus, a model
including these dummy variables would not be identified.
Given (1'), the individual coefficients P3ik are the derivatives of the log odds ratio between
alternatives =1,2 and alternative 0 with respect to explanatory variable k:
S n P(PLAN, 1 (9)
jxk [P(PLAN,t = 0)
Similarly, (31k P2k) gives the derivative of the log odds ratio between alternatives 1 and 2 with
respect to explanatory variable k:
lk a In[P(PLAN, = 1) (10)
axk k nP(PLAN, = 2)]
For purposes of interpretation, it should be noted that the coefficients themselves do not give the
marginal effects of the independent variables on the individual probabilities. The marginal
effects need not even have the same sign as the coefficient. For expository purposes, I will refer
to coefficients in the vector P3i as coefficients in the ESR equation since they give the derivative
of the log odds ratio between ESR and RORR. Similarly, I will refer to coefficients in the vector
P2 as coefficients in the PCR equation.
I now proceed as follows. First I briefly enumerate the explanatory variables use to capture
the theoretical effects identified above and discuss the temporal composition of the panel of
independent variables. Then, I present the detailed definition of each explanatory variable and
discuss the empirical findings regarding that variable before turning to the definition of the next
variable. The explanatory variables used are: aggregate experience with ESR and PCR
(ESRYEARS and PCRYEARS), the regulatory authority's budget (BUDGET), a measure of
party dominance (CONTROL), a measure of the strength of organized labor (UNION), state
personal income (INCOME), a measure of labor costs (HSEARN), the percent of the state's
24 See Greene (1993) or Madalla (1983) for a detailed discussion of the multinomial logit model.
population that resides in metropolitan areas (%METRO), the frequency of rate filings
(RATECASE), the number of registered lobbyists per state legislator (LOBBY), the historical
maximum allowed rate of return on rate base (AROR), and the average educational attainment of
citizens in the state (EDUCATION). The hypothesized effects of ESRYEARS, PCRYEARS,
and CONTROL are all time sensitive, so these variables vary with time by construction.
BUDGET, RATECASE, and AROR are based on historical figures and do not vary over time.
Since these variables are all used to proxy more primitive forces that should not vary much over
short periods of time, this should retain the needed explanatory power while avoiding potential
simultaneity problems. HSEARN and EDUCATION are based on the 1990 Census and so do
not vary over time. Similarly, LOBBY is available only for 1991 and so does not vary over time.
INCOME, %METRO, and UNION are available over time. However, since these variables are
used to proxy forces that should not change much over short periods of time, I use 1990 values
for INCOME and %METRO and the available year nearest 1990, 1989, for UNION.25 I proceed
by defining each independent variable and discussing the empirical findings regarding that
variable before moving on to the next variable definition. Descriptive statistics are presented in
Table 2 below.
Table 3 contains the results of the multinomial logit estimation. The first three columns
contain the estimates of the coefficients in the ESR and PCR equations, respectively. The third
column gives the difference between the coefficients in the PCR equation and the corresponding
25 Time series data for INCOME is available based on the Survey of Current Business published
by the Department of Commerce. However, the full series is noisy and is regularly revised,
while most revisions to the 1990 figures should have been completed by the time of this
research. Similarly %METRO and UNION are available based on the Current Population
Survey, but the figures are quite noisy due to the small sample size in many states. If the time
series data for these variables are used, the results presented below do not change qualitatively,
but the statistical significance of the model is slightly reduced by the additional noise in the data.
coefficients in the ESR equation. The numbers in parentheses below the coefficients and
coefficient differences are pvalues. The final three columns of Table 3 provide an estimate of
the magnitudes of the effects of changes in the independent variables. With two exceptions,
noted below, these figures give the increase in the probability of each type of plan when the
indicated variable is increased from the 40t percentile of the sample to the 60 with all other
variables evaluated at the sample medians.
TABLE 22
SAMPLE DESCRIPTIVE STATISTICS
Variable Mean Standard Minimum 40th % Median 60th % Maximum
Deviation
ESRYEARS 69.143 39.336 14.000 47.000 67.000 90.000 128.000
PCRYEARS 7.714 8.025 .000 2.000 5.000 8.000 24.000
BUDGET 1.918 1.351 .269 1.248 1.457 1.809 5.877
CONTROL .387 0.418 .000 .000 .500 .500 1.000
UNION 18.349 11.416 2.900 12.850 15.900 19.400 51.600
INCOME 101.156 114.105 7.700 51.050 60.300 84.450 617.700
HSEARN 30.743 2.852 26.007 29.699 30.301 31.029 37.755
%METRO 69.073 20.807 23.900 67.850 69.800 79.600 100.000
RATECASE .844 .632 .000 1.000 1.000 1.000 2.000
LOBBY 5.685 4.937 .500 3.950 4.400 4.700 28.000
AROR 11.462 .944 9.310 11.545 11.750 11.938 12.700
EDUCATION 12.441 .425 11.534 12.365 12.496 12.560 13.207
The entries at the bottom of Table 3 indicate that the model is highly significant overall and
the predicted values from the model correctly classify 73.2% of the observations while only
49.8% would be correctly classified by predicting that every observation would adopt RORR, the
modal regime. Most of the hypotheses implied by the model of the previous section are
statistically supported and none are statistically contradicted. Table 4 tabulates actual versus
predicted regulatory regimes. Observation by observation inspection of incorrect classifications
revealed no discernable pattern in state by state classification errors.
TABLE 23
MULTINOMIAL LOGIT ESTIMATION RESULTSa
Coefficients
_ESR PPCR
ESRYEARS
PCRYEARS
BUDGET
CONTROL
UNION
INCOME
HSEARN
%METRO
RATECASEc
LOBBY
ARORd
ARORSQ
EDUCATION
Observations
Log Likelihood
X2
P(02)
Pseudo R2
% Correct
Predictions
.155
(.001)
1.466
(< .001)
.218
(.439)
2.084
(.010)
0.251
(< .001)
.013
(.008)
.720
(.001)
.113
(.005)
.395
(.499)
.225
(.023)
78.071
(.001)
3.368
(.001)
6.283
(< .001)
209
126.980
174.310
< 0.001
0.407
73.206
.006
(.644)
.077
(.232)
.332
(.027)
.113
(.824)
.015
(.522)
.003
(.442)
.283
(.035)
.008
(.593)
.790
(.015)
.030
(.494)
3.626
(.471)
.153
(.498)
2.876
(< .001)
PPCRESR
.149
(.002)
1.543
(< .001)
.114
(.705)
2.196
(.011)
.266
(< .001)
.016
(.002)
.437
(.059)
.105
(.012)
1.185
(.054)
.255
(.014)
81.696
(< .001)
3.521
(.001)
3.408
(.021)
Magnitudesb
RORR ESR PCR
.763 .928
.744 .977
.032 .021
.165
.185 .239 .054
.307 .393
.087 .116
.086
.029
.203 .217 .014
.250 .305
.063 .125
.055
.062
.033 .043 .010
.346
[.176]
.505
[.224]
.253 .268
.159
[.048]
.014
a Numbers in parentheses below coefficients are pvalues for a two tail test.
b Estimated change in probability from increasing the independent variable from the 40th
sample percentile to the 60th, all other variables at the sample median, except for
RATECASE and AROR. See c and d below.
For RATECASE, both the 40th and 60th percentiles are 1. The changes listed are for an
increase from 1 to 2.
d The first set of numbers in the last three columns are for an increase from the 20th to the 40th
percentile. The numbers in brackets are for an increase from the 60th percentile to the 80th.
TABLE 24
PREDICTED VERSUS ACTUAL REGULATORY REGIMES
Predicted Regime
RORR ESR PCR
Actual RORR 84 9 11
Regime ESR 7 30 2
PCR 26 1 39
ESRYEARS (PCRYEARS) is the total number, over all states, of years that ESR (PCR) was
in effect up to two years before the state's regulatory plan went into effect. For example, in 1990
and 1991 1 state operated under PCR, so PCRYEARS would equal 2 for states whose regulatory
plans went into effect in 1993. In 1992, 3 states operated under PCR, so PCRYEARS would
equal 5 for states whose regulatory plans went into effect in 1994. These variables are
constructed in this manner because when planning for a regime the year before it goes into
effect, regulators and firms can draw on experience cumulative through the year prior to that.26
As experience with alternative regulatory structures increases, it becomes easier for states to
structure their own plans, so transition costs decline. Thus, Observation 1 suggests that the
coefficient on ESRYEARS in the ESR equation should be positive and larger than the coefficient
in the PCR equation. Similarly, the coefficient on PCRYEARS in the PCR equation should be
positive and larger than the equation in the ESR equation. The signs of the coefficients and
coefficient differences reported in Table 3 agree with all of these predictions and all of the results
except the coefficient on PCRYEARS in the PCR equation for which a hypothesis was expressed
are statistically significant at conventional levels. The final three columns of Table 3 indicate
that the magnitude of the effect of increases in experience is quite substantial.
26 Using a one period lag instead of a two period lag does not effect the results qualitatively.
BUDGET is the average budget of the state regulatory commission in 1984 and 1985 (when
all states operated under rate of return regulation) expressed in per capital terms.27 Regulatory
budgets prior to 1986 are used because the regulatory budget is probably influenced by the type
of regulatory plan in place as well as the plans being considered for the near future. Higher
regulatory budgets should increase knowledge and reduce uncertainty about costs, demand, and
how to implement regulatory alternatives. Thus, increases in BUDGET might reflect reduced
transition costs and lower uncertainty. If this is the case, Observation 1 and Observation 2
suggest that the coefficients in both the ESR and PCR equations will be positive.28 However,
large budgets might also reflect an entrenched bureaucracy with an interest in maintaining the
status quo and thus higher transition costs. Similarly, low regulatory budgets might reflect
environments in which regulators are severely resource constrained. Regulators in such a
situation might wish to implement a more streamlined regulatory alternative. Both of these
possibilities would tend to counter the knowledge effect described above. Both of the BUDGET
coefficients are positive, as predicted, but only the PCR coefficient is significant. Compared to
the other variables, the magnitudes of the effects of BUDGET are relatively small.
27 Source: National Association of Regulatory Utility Commissioners (1984 and 1985).
BUDGET reflects commission expenditures, not the actual budget allocation. While both series
are available, there are more missing data for the budget allocation. Of the 45 states in the
sample, actual expenditures were missing only for Arizona and Louisiana. For these states,
however, the budgetary allocation was available. The actual expenditure for the state was then
estimated by multiplying the budget allocation by the average percent of the budget allocation
actually spent in the year in question (across states for which both observations were available).
As it probably requires more effort to regulate larger firms, or more firms where applicable,
budget must be corrected for the size of the firms' operations within the state, thus I express
BUDGET in per capital terms.
28 Zearfoss (1998) finds that regulatory budgets are an important determinant of regulatory
performance.
CONTROL averages the one period lag and three period lag of a variable that is 1 if either
the Democratic party or the Republican party controls both houses of the state legislature and the
governor's office and 0 otherwise.29 Since legislative terms at the state level typically last two to
four years, averaging the one and three period lags reflects the composition of the last two
legislative assemblies. Control by one party might indicate a more stable political environment
and might therefore make passage of any enabling legislation needed to implement a new
regulatory regime easier. To the extent that this lowers transition costs, Observation 1 suggests
both coefficients on CONTROL should be positive. The coefficient in the ESR equation is
positive and statistically significant while the coefficient in the PCR equation is negative but
statistically insignificant. The fourth column of Table 3 indicates that the magnitude of the
decrease in the probability of RORR associated with increases in CONTROL is of moderate size
relative to the other variables in the model.
UNION is the percent of manufacturing employees in the state that were union members in
1989.30 Since there is little incentive to contain costs under RORR, telecommunications workers
may have received substantial rents under traditional regulation. If this is the case, they may
resist implementation of a regulatory regime that would create incentives to contain labor costs.
Therefore, transition costs will be higher in states where organized labor is stronger due to
opposition from this interest group.31 Thus, both coefficients on UNION should be negative.
Table 3 reveals that the coefficient in the ESR equation is negative and statistically significant
29 Source: U.S. Department of Commerce, Statistical Abstract of the United States, 19891997.
30 Source: U.S. Department of Commerce, Statistical Abstract of the United States, 1992.
31 While it is possible to get industry specific data on union membership, the more aggregate
measure used here is more reflective of the strength of organized labor within a state. In a states
where organized is not important, one would not expect union membership in the
telecommunications industry to have much of an impact.
while the coefficient in the PRC equation is positive but insignificant. The fourth column of
Table 3 shows that the positive effect of increased unionization on the probability of RORR is
fairly large in magnitude.
I use three variables to proxy the potential benefits of improved incentives for cost reduction
(b). INCOME is the state's personal income in 1990, measured in billions of dollars.32 It seems
reasonable to expect that the possible efficiency gains from adopting some form of alternative
regulation should increase with the size of the market in the state. HSEARN is the 1989 average
annual earnings of male high school graduates age 35 to 44 in thousands of dollars.33 HSEARN
should provide a measure of the cost of constant quality labor across states. Where labor costs
are higher, the potential gains from allocating labor efficiently should be larger. %METRO is
the percent of the state's 1990 population contained in metropolitan areas.34 If there are
economies of scale in local operations, or if metropolitan markets of the same size are more
profitable due to the concentration of economic activity, the potential benefits of alternative
regulation will be higher when %METRO is higher. To the extent that these variables capture
the potential benefits from adopting an alternative form of regulation, Observation 3 suggests
that the coefficients on each variable in the ESR and PCR equations should be positive. These
predictions receive strong support in Table 3. Of the six coefficients, only the coefficient on
INCOME in the PCR equation has the wrong sign, and it is insignificant. Of the five coefficients
with the predicted sign, only the PCR coefficient on %METRO is statistically insignificant. The
32 Source: U.S. Department of Commerce, Statistical Abstract of the United States, 1997.
33 Source: U.S. Department of Commerce, data collected for the 1990 U.S. Census.
34 Source: U.S. Department of Commerce, Statistical Abstract of the United States, 1997
coefficients on INCOME and %METRO in the PCR equation may fail to support Observation 3
because they also proxy the political strength of consumers to some degree, and the effects of the
relative political strength of consumers and the firm are theoretically ambiguous.35 All of these
variables lead to declines in the probability of RORR that are moderate in magnitude compared
to the other variables in the model.
The variable RATECASE records the number of rate filings in each state from 1984 to
1985.36 Like BUDGET, RATECASE incorporates only pre1986 data to avoid endogeneity
problems. Higher numbers of rate cases probably reflect higher levels of uncertainty (higher c),
a higher probability that a rare event will occur (higher 4), and a higher probability that a hearing
will be needed when a rare event occurs under RORR (higher 8). Therefore, while an increase in
RATECASE might either increase or decrease the likelihood of ESR or PCR relative to RORR,
Observation 2 and Observation 4 suggests that it will decrease the likelihood of PCR relative to
ESR. The information recorded in Table 3 supports this hypothesis, as the coefficient on
RATECASE in the PCR equation is statistically smaller than the coefficient in the ESR equation.
This finding is also, of course, consistent with the hypothesis that more rate cases simply indicate
a regulator that wants to keep closer control over the firm, thus preferring ESR to PCR. The
magnitude of the effect of an additional rate case is modest relative to the effects of the other
independent variables.
35 Income depends upon both percapita income and population. Foreman (1995) found evidence
that intraLATA toll rates were lower where percapita incomes were higher. This might be
because larger consumers of intraLATA service exert more pressure for low rates. HSEARN
reflects not only labor costs, but also the value of time. Filer, Kenny, and Morton (1993) find
that the average citizen exerts less political influence when the value of their time is higher.
%METRO reflects the geographic concentration of consumers. Many studies, including Stigler
(1971) and Becker (1986) have found that interest groups are more effective when they are more
concentrated geographically.
LOBBY is the number of registered lobbyists per state legislator in each state in 1991.37 In
states where there are more interest groups competing for influence, it seems quite likely that
there will be more groups seeking to influence regulatory proceedings and to be heard at
regulatory hearings. Thus, negotiation and political costs associated with the regulatory process
(kcs and kV) may be higher in states where LOBBY is higher. It would be better to have a direct
measure of the number of groups actively seeking to exert influence on telecommunications
issues, but such data are not available. Observation 4 thus implies that increases in LOBBY
should make PCR less likely relative to RORR, and the estimated coefficient in the PCR
equation is statistically smaller than the coefficient in the ESR equation. The magnitudes of the
effects of LOBBY are modest relative to the other variables.
Observation 5 indicates that decreases in the probability that additional hearings would be
needed under RORR when a rare event occurred (8) make RORR more attractive relative to both
ESR and PCR. However, it is difficult to obtain a variable that might proxy this probability that
is also independent of the probability of a rare event. One might hypothesize that when one
group is dominant in the regulatory process, decisions favoring that group will seldom be
challenged and the regulator may be able to accommodate the wishes of the dominant group
when a rare event occurs without additional hearings. If this is the case, the possibility of rare
events will tend to make RORR more attractive relative to ESR and PCR when either group
dominates the regulatory process. Further, when either group dominates the process, the costs of
regulatory proceedings may be lower for the same reasons, making PCR more likely relative to
ESR.
36 Source: National Association of Regulatory Utility Commissioners (19821985).
37 Data for LOBBY is taken from Morgan et al (1993).
To capture this possibility, I include AROR and its square, ARORSQ, in the model. AROR
is the maximum rate of return on rate base allowed by the regulatory authority, averaged over
1984 and 1985.38 Equation 5 shows that the target earnings level approved by the regulator
under RORR (E) will become small when the weight the regulator places on consumer surplus
is very large relative to the weight she places on profit. Similarly, it will be limited only by the
reservation value of the service, as the weight placed on consumer surplus becomes very small.
Therefore, extremely low values of AROR may be associated with consumer dominance while
extremely high values may be associated with firm dominance.
To the extent that extreme values of AROR correspond to states where additional hearings
are less likely to be needed under RORR when a rare event occurs, Observation 5 suggests that
both coefficients on AROR should be positive while both coefficients on ARORSQ should be
negative. To the extent that extreme values of AROR indicate lower costs of regulatory
proceedings, Observation 4 suggests that the coefficient on AROR in the PCR equation should
be smaller than its coefficient in the ESR equation. Similarly the coefficient on ARORSQ in the
PCR equation should be smaller than its coefficient in the ESR equation. This is because ESR
economizes on the costs of hearings to deal with rare events relative to RORR. This effect might
tend to counter the previous one though since the effect of higher costs of regulatory proceedings
on the choice between RORR and ESR or PCR is ambiguous. Inspection of Table 3 shows that
the coefficient on AROR in the ESR equation is indeed positive and larger than the coefficient in
the PCR equation. The combined effect of AROR and ARORSQ changes sign when AROR
equals 11.59. Similarly, the coefficient on ARORSQ in the ESR equation is negative and
smaller than the coefficient in the PCR equation and the combined effect changes sign at 11.85.
38 Source: National Association of Regulatory Utility Commissioners (1984 and 1985).
Each of these results is statistically significant. The coefficients in the PCR equation do not have
the predicted sign pattern overall, but neither is significant statistically. The figures in the last 3
columns of the AROR row give the estimated effects of increasing AROR from the 20th sample
percentile to the 40th, with all other variables evaluated at their sample medians. This change
gives rise to a large decrease in the probability of RORR and a large increase in the probability
of ESR. The figures in brackets in the next row give the estimated effects of increasing AROR
from the 60t sample percentile to the 80 with all other variables evaluated at their sample
medians. This change results in a moderate increase in the probability of RORR and a moderate
decrease in the probability of ESR.
EDUCATION is the mean number of years of education of the citizens in the state in 1990.39
A more educated populace should be more able to promote its interests. Thus, in states where
EDUCATION is higher, the relative political strength of consumers should be higher. I thus
include EDUCATION as an additional control for the (theoretically ambiguous) effects of the
relative political strength of consumers and the firm. Education might also reflect higher
potential benefits from providing incentives for more efficient operation. The empirical results
indicate that higher levels of education tend to make RORR more likely relative to both ESR and
PCR and PCR more likely relative to RORR. While the coefficients on EDUCATION are highly
significant, the magnitudes of its effects on regime adoption are moderate relative to the other
variables.
39 Source: U.S. Department of Commerce, 1990 U.S. Census. EDUCATION is calculated from
reported categorical data.
Conclusion
I developed a simple theoretical model of regulatory regime adoption and used it to inform
an empirical investigation of intrastate telecommunications regulation. My work adds to that of
Donald and Sappington (1995 and 1997) on regime selection in two important respects. First, I
allow for important differences between the two dominant alternatives to traditional rate of
return regulation. Second, I give more explicit consideration to the role of uncertainty, political
concerns, and the possibility of unplanned for contingencies (Zfactors). I find that regime
adoption patterns can be explained fairly well using the theoretical differences in the incentive
properties of regulatory alternatives and a simple theory of the political economy of regulation.
The empirical model is highly significant overall. Most of the predictions of the theoretical
model were confirmed statistically and none were statistically contradicted.
Several empirical regularities consistent with the theoretical predictions of my model
emerged, including the following. The empirical relationships between regime adoption and
experience, regulatory budgets, and union strength are consistent with the simple notion that a
state will be less likely to switch from RORR when transition costs are higher. The size of the
market as reflected by total state personal income, labor costs as reflected by the annual earnings
of earnings of high school graduates, and the percentage of the population residing in
metropolitan areas were found to be positively related to the adoption of an alternative to RORR.
This evidence supports the hypothesis that an alternative form of regulation will be more likely
relative to RORR when the potential benefits from improved incentives are larger.
I found the historical incidence of rate cases to be significantly related to regime adoption. In
particular, ESR was found to be more likely relative to PCR when more rate cases were filed in
the past. This is consistent with both the hypotheses that ESR economizes on regulatory costs
due to unforeseen contingencies (Zfactors) relative to PCR and the hypothesis that ESR reduces
the adverse effects of uncertainty relative to PCR. Finally, I found that the number of registered
lobbyists per legislator in a state was a significant determinant of regime adoption. In particular,
ESR was found to be more likely relative to PCR when there are more registered lobbyists per
legislator. More lobbyists per legislator may indicate an environment in which regulatory
proceedings are more costly because more groups are competing for influence and placing
demands upon the regulator's and the firm's time. If this is the case, this finding provides further
support for the hypothesis that ESR will be more likely relative to PCR when it is more desirable
to economize on regulatory costs.
The analysis presented here implies that recent changes in regulatory institutions in the
telecommunications industry and the current prevalence of PCR are more than simple stepping
stones on the way toward less intrusive regulation and finally deregulation. While regulatory
regimes may have moved in that general direction, the growth of alternative regulatory regimes
has been fueled at least in part by reductions in transition costs due to a gradual accumulation of
experience. Further, the path states take when moving toward less intrusive forms of regulation
is influenced in fairly intricate but, at least in part, reasonable and predictable ways by its
economic and political circumstances. These findings may allow a better understanding of
regulatory change in other industries.
There are, of course, a number of avenues for future work on regulatory regime adoption in
the telecommunications industry. While the 3way classification used here is more general than
past investigations, there are wide variations across plans of a particular type. A more complete
exploration of regime adoption might examine approved rates or return and rate base in rate of
return states, the determination of specific sharing rules in earnings sharing states, and the initial
60
level of and adjustment mechanisms for prices in price cap plans. All of these things are part of
the full character of a regulatory regime. In addition, if the expected wave of deregulation does
materialize, analyzing movement all the way from RORR to deregulation will be a logical step to
take.
CHAPTER 4
THE INEFFECTIVENESS OF SCHOOL INPUTS:
A PRODUCT OF MIS SPECIFICATION?
Introduction
Many academics seem to have accepted Hanushek's (1986, p. 1162) conclusion that "there
appears to be no strong or systematic relationship between school expenditures and student
performance (italics in original)." Hanushek's rather startling statement concludes his review of
65 regressions, found in over a dozen articles, estimating how school expenditures affect
educational outcomes. Although this conclusion is now widely accepted by economists, voters
continue to ratify sizable educational budgets and spend more on education when they have more
income. Real spending per pupil has tripled since 1960. Given this preference for increased
spending, perhaps it is premature to conclude that school inputs are ineffective. In this paper, I
reexamine the educational production function literature, focusing on the role of specification in
determining the significance of education inputs.
Estimates from an educational production function are most commonly used to assess the
efficacy of primary and secondary school inputs on educational output. This production function
relates a measure of educational output (e.g., standardized achievement test scores, graduation
rates, attendance/dropout rates, or post school economic achievements) to a set of inputs. The
parental, student, and school inputs appropriate for these studies must reflect the fact that before
and during the primary and secondary years knowledge is produced both at home and at school.
Following standard production function theory, each input is expected to boost learning.
Children should acquire more knowledge when their parents spend more time with them
developing their skills, and more educated parents are expected to be more effective in passing
on knowledge. Similarly, students should learn more when they spend more time in class
learning from teachers, at home being tutored by their parents, or studying by themselves.
Students are expected to learn more from better teachers and in smaller classes, where each
student gets more attention. Though it may be less obvious why there should be higher
achievement in larger schools, Kenny (1982) shows that the cost of any level of achievement is
minimized by expanding the area served by a school until the increase in transportation costs per
student is equated to the savings in inschool costs that accompany a larger school. This
reduction in inschool costs implies that schools should operate in a region of increasing returns
to scale and accordingly that students should learn more in larger schools, holding other inputs
constant. 1
The lack of support for these predictions in the education production function literature may
be caused by misspecification. In two thirds of the studies that I analyze below, family income
or socioeconomic status has been included as an independent variable. Perhaps this stems from a
belief that family factors "tend to be highly correlated with socioeconomic status of the family"
[Hanushek (1971, p. 281)] and therefore either income or socioeconomic status can be used as a
proxy for any inputs which families might provide outside of the school environment but which
are difficult to identify and measure. In the usual household production model, however, the
parental time and income budget constraints determine the time parents spend with each child
1 Although a number of papers provide support for this prediction, other research finds that costs
fall and then rise as schools become larger. This literature is summarized in Cohn and Geske
(1990), pp. 205207.
and quality of the school system.2 In a Tiebout (1956) setting, parents select school inputs
through the choice of the community; parents demanding better school locate in school districts
that provide better schools. Accordingly, it makes no sense to include family income in an
educational production function along with the parental and educational inputs that are jointly
determined by family income.
I show in the next section that the inclusion of the demand variable family income creates
serious statistical problems that should make it more difficult to conclude that school inputs are
significant. A few researchers have recognized this specification problem. Strauss and Sawyer
(1986, 42), noting an "extensive public finance literature [in which] income [would be] a causal
factor in the expenditure equation," conclude that educational production functions with income
and educational expenditure mix a "demandforpublicgoods relation ... and a production
relation." They examine the impact of deleting income from the estimated production function.
Unfortunately, their regressions do not include measures of parental or student time inputs.
GyimahBrempong and Gyapong (1991) also recognize the endogeneity of these school inputs.
They agnostically estimate the effect of dropping four socioeconomic measures  family
income, parental educational attainment, poverty rate, and crime rate  from their regressions.3
Their results suggest that multicollinearity between income and school spending leads to a
negative coefficient on spending when income is included and a positive coefficient when
income is excluded. Further, they find that dropping parental education results in a statistically
2 See, for example, Kenny (1982) and similar models in DeTray (1973), Willis (1973), and
Becker (1991).
3 It makes little sense to drop educational attainment, which measures effective parental time.
significant loss of explanatory power in all cases, while all of the others can be dropped with no
loss if parental education is retained.4
Although these studies, particularly the GyimahBrempong and Gyapong paper, suggest that
including income may contribute to concluding that school inputs are ineffective for student
achievement, there is no systematic evidence on whether this form of model misspecification is a
problem. I provide evidence on this issue, using a variety of statistical techniques. In the third
section of the paper, I summarize, using metaanalysis, the empirical findings from a larger set of
papers than Hanushek (1986) examined. Each regression studied is classified as either correctly
specified (i.e., a "good" study) or misspecified (i.e., a "bad" study), and results for the two types
of studies are compared. In the fourth section, I estimate two educational production functions,
using the Project TALENT micro data set and pooled statelevel data, to determine directly the
sensitivity of my parameter estimates to various specification errors involving including income.
The results of the metaanalysis and my regressions support my assertion that misspecification
has played an important role in concluding that school inputs do not matter. I also use an
instrumental variables procedure to deal with potential bias of the school input coefficients and
find evidence of an endogeneity problem and that school input coefficients in even the better
specified education productions appear to be biased downward.
4 In a related vein, Hanushek (1996, p. 21) claims that school inputearnings studies are marred
by the omission of any parental input measures, which leads to overstatement of the impact of
school inputs.
The Statistical Effects of Including Demand Variables
To illustrate the specification issues, consider the following simple household production
model. The parent's utility depends on how much the child learns (L) and other consumption
(C).
U = U(L, C) (1)
Each is produced in a household production function. The education production function is
L = f(S, tL; E) (2)
where S represents the quality of the school system, tL the amount of time the parent spends
teaching the child, and E the educational attainment of the parent. An increase in the parent's
education is expected to raise the productivity of his or her time spent teaching the child.5 This
formulation reflects the reasonable belief that virtually all of the parent's direct impact on the
child's learning occurs through the quality and quantity of time spent with the child.6 Similarly
the production function for other consumption is
C = g(X, tc; E) (3)
where X is the amount of goods purchased and tc is the time devoted to other consumption.
5 There is substantial evidence that those who are more educated are more productive or more
efficient. The labor market acts as if this is true in the work place, since wage rates rises with
education. Michael (1973) found that the effect of education on the demand for goods, holding
income constant, was consistent with a model of household production in which education raised
household productivity neutrally. Those who are more educated are more adept at dealing with
disequilibria [Schultz (1975)], are better informed about the voting record of their Senators
[Husted, Kenny, and Morton [1995]) and more likely to not reelect Senators who have been too
liberal or conservative for their constituency [Schmidt, Kenny, and Morton (1996)].
6 Murnane, Maynard, and Ohls (1981, p. 369) found no evidence that purchased household goods
affect achievement.
The parent faces the time and goods budget constraints:
T = tL + tc + tw, (4)
where tw is the time spent working and T is available time, and
PsS+ X = w.tw (5)
where Ps is the price of school quality in terms of X and w is the hourly wage rate. Substituting
(4) into (5) produces the full income constraint:
(PsS + wtL) + (X + wtc) = w.T (6)
This shows how potential income is allocated to the time and goods inputs into learning and
other consumption.
Maximizing utility (1) subject to the production functions (23) and the full income
constraint (6) yields the demand functions for the two outputs and their inputs:
L = DI(T, w, Ps, E)
C = D2(T, w, Ps, E)
S = D3(T, w, Ps, E)
X = D4(T, w, Ps, E)
tL = D5(T, w, Ps, E)
tc = D6(T, w, Ps, E)
Note that all outputs and inputs are determined by the same set of variables.
Now I can consider the issues involved in estimating the education production function (2).
Suppose I first linearize it [ignoring error terms for the time being].
L = bo + blS + b2tL + b3E (7)
I am aware of no data set that has ideal measures of all the variables entering the education
production function. A few data sets examining the skills of young children have qualitative
information on the time the mother spends teaching the child but do not have good information
on the child's school. The data sets with good information on schools have no direct measures of
how much time the parents spend teaching their children (tL). If a parental labor force measure
(such as tw) is available, it can be used as an instrument for tL in (7), since it is clear from the
time budget constraint (eq. 4) that these tend to be negatively correlated. The Project TALENT
regressions that I report later use this strategy.
Suppose more typically that there is no parental labor force variable. There are several ways
in which to deal with this problem. Most commonly, the production function is estimated using
a measure of the parent's income, such as w, presumably as a proxy for tL. Then
L = bo + blS + b3E + b4w (8)
The problem with this solution is that w is unlikely to be a good proxy for the parent's time
teaching the child. Conflicting income and substitution effects accompany an increase in the
wage rate, making the net effect on tL quite uncertain.
Moreover, the introduction of w into the production function introduces multicollinearity
between w ("income") and the school quality S that it determines via the demand function D3.
Since income is an important determinant of school quality, this problem will be severe. As
multicollinearity may already be present in these models, the estimators may lack precision even
without the inclusion of income. Adding income then might doom one to finding school inputs
to be irrelevant, even when they are in fact highly productive. Inspection of the expression below
for the variance of the jh coefficient under standard ordinary least squares assumptions will make
the severity of this problem apparent. Here, 02 is the variance of the error term and Rj2 is the R2
from an auxiliary regression of Xj on all of the other explanatory variables.
2
Var[3j]=
(1Rf)1i(XirXj)2
Obviously, the inclusion of income will increase Rj2, probably by a large amount. An
analogous result may be obtained for the estimated variance as well.7 Inclusion of income thus
will increase the dispersion of estimates obtained from repeated regressions and increase the
estimated standard errors in each individual regression. This means that more negative
coefficients and fewer significant coefficients will tend to be found when income is included.
The subsequent analysis provides evidence on these assertions.
Alternatively, the production function can be estimated without a measure of how many
hours the parent spends with the child:
L = bo + blS + b3E (9)
The major econometric concern over this solution is the bias in the school quality coefficient due
to omitting tL. Since the correlation between school quality and parental time spent teaching the
child could be positive or negative, it is unclear whether the school quality coefficient is upward
or downward biased. If the correlation is positive, the coefficient will tend to be upward biased.
A third strategy is to use an instrumental variable procedure to estimate the demand function
for school quality (D3) and then use the predicted values for school quality (S') to estimate a
production function that does not include a measure of parental hours.
7 See Greene (1993, pp. 248, 267) for a thorough presentation of these issues.
L = bo + biS'+ b3E (10)
This procedure, followed in Kenny (1980) and in Section IV below, should produce unbiased
school quality coefficients. Its success, of course, hinges on using good instruments for school
quality.
Meta ReAnalysis of the Education Production Function Literature
To examine the production of knowledge before the child leaves the nest, I confine my
analysis to studies that examine cognitive skills, as measured by a score on a standardized test.
Hypotheses about various school inputs are confirmed in some studies but not others. To allow
testing for overall significance, I require that the result appear in a table in which the tratio was
reported or from which could be calculated.8 Thus, anecdotal statements that a variable was
insignificant in unreported regressions were ignored; as Hedges, Laine, and Greenwald (1994b,
p. 9) note, in these situations "even the specification of the model was often unclear." I omitted
these "results" because the level of significance could not be determined and furthermore
because it is unclear how including the variable would have affected the significance of those
variables that were included in the regression. Many studies report more than one regression. If
a paper reports several regressions using the same dependent variable and sample, only the "best"
regression is utilized. On the other hand, regressions based on different dependent variables (for
example, math and reading scores) and/or samples (e.g., based on grades or geographical area)
provide complementary statistical evidence. Accordingly, each of these contributes potentially
one observation to my analysis. The tables that follow are based on 127 regressions taken from
8 Similarly, if a variable and its square appeared in the regression and the estimated effect
changed sign within the range of the sample, the results were excluded. In this case, it was
impossible to ascertain significance from the reported results.
46 papers. Note that Hanushek's (1986) analysis is based on 147 regressions from 33
publications. My study includes the 28 papers he surveyed which included regressions meeting
my criteria as well as 18 other papers.
These papers examined the impact of a variety of educational inputs. I collected results for
teacher experience, teacher education, other teacher characteristics (e.g., teacher test score,
ranking of teacher's college), teacher salary, teachers per pupil, expenditure per pupil, and school
size. If a regression included several variables from one category, such as science class size and
nonscience class size, the result for each variable was collected.
Classification of the regressions as correctly or incorrectly specified was based upon
inclusion of appropriate variables to measure the impacts each type of input. Many studies did
not include any measure of the time students devoted to learning. However, I did not use this as
a sorting criterion because such data have not commonly been available. All of the studies I
examine consider the impact of school resources. The actual screening then centered upon two
criteria related to family inputs. The first reason for labeling a regression "bad" was outright
failure to include some direct measure of parental contribution, such as parent's education and/or
parent's hours worked. The second reason was inclusion of income or socioeconomic status,
which as noted above are demand variables instead of input measures.
Under these two weak criteria (failure to include a measure of parental inputs and inclusion
of income or socioeconomic status) 92 of the 127 studies, nearly three quarters, were labeled as
bad. Income or socioeconomic status was included in 85 studies; 7 of these also did not have a
variable specifically measuring parental inputs. Seven other studies were labeled as bad due to
the omission of any parental input measure.9 Misspecification, particularly the inclusion of
income as a regressor, thus appears to be a serious problem in this literature.
TABLE 31
META REANALYSIS: COEFFICIENT SUMMARIES
A: ALL 127 REGRESSIONS
1TAIL SIGNIFICANCE:
TEACHER EDUCATION
TEACHER EXPERIENCE
TEACHER SALARY
OTHER TEACHER CHAR.
TEACHERS PER PUPIL
EXPENDITURE PER PUPIL
SCHOOL SIZE
TOTAL
1TAIL SIGNIFICANCE:
TEACHER EDUCATION
TEACHER EXPERIENCE
TEACHER SALARY
OTHER TEACHER CHAR.
TEACHERS PER PUPIL
EXPENDITURE PER PUPIL
SCHOOL SIZE
TOTAL
POSITIVE
<2.5% 2
11
27
7
33
11
21
15
125
`E NEGATIVE
.55% INSIG. INSIG.
7 25 12
2 15 15
3 3 6
5 28 8
5 30 10
1
4
27
13
19
133
B: 35 GOOD REGRESSIONS
POSITIVE NEGATIVE
<2.5% 2.55% INSIG. INSIG.
3 0 5 3
12 0 3 5
0 0 0 0
4 35
<5%
9
5
3
2
6
4
25
54
<5%
1
3
0
1 0
3 2
1 1
4 2
17 9
C: 92 BAD REGRESSIONS
POSITIVE
1TAIL SIGNIFICANCE:
TEACHER EDUCATION
TEACHER EXPERIENCE
TEACHER SALARY
OTHER TEACHER CHAR.
TEACHERS PER PUPIL
EXPENDITURE PER PUPIL
SCHOOL SIZE
TOTAL
NEGATIVE
<2.5% 2.55% INSIG.
8 7 20
15 2 12
7 3 3
23 4 21
8 3 23
17 0 7
7 4 12
85 23 98
Note: significance level is based on a onetail test.
9 As Hanushek (1996, p. 21) notes, the importance of school inputs should be overstated in
studies with no parental measure. Nevertheless mixing these 7 studies that favor education
unduly with the 85 that I argue are biased against school inputs does not affect my empirical
TOTAL
64
64
22
76
62
43
83
414
TOTAL
12
23
0
19
17
13
21
105
INSIG.
9
10
6
7
7
3
16
58
<5%
8
2
3
2
4
3
23
45
TOTAL
52
41
22
57
45
30
62
309
The 414 coefficients from the 127 regressions are classified according to sign and
significance level in Table 31. The reported significance levels are based on a onetail test;
given the presumption that inputs have positive marginal products, such a test is appropriate. In
Tables 32 and 33, my results are further summarized by sign and significance level,
respectively, and compared with Hanushek's (1986) summaries.
If school inputs were truly ineffective, only half of the coefficients would be positive. The
fact that over two thirds (68.8 percent) of my coefficients, collected for the reanalysis, have the
expected positive sign suggests that school inputs have a positive impact. Over 81 percent of the
coefficients for expenditure per pupil and for other teacher characteristics (e.g., teacher test
scores) are positive, but less than half the coefficients for school size are so. Hanushek, on the
other hand, found only 56.1 percent of the coefficients to be positive in the studies he examined.
The coefficients on teacher education, teachers per pupil, and expenditure per pupil were much
less often positive in his summary than in the group of papers I examined.
TABLE 32
META ANALYSIS: COEFFICIENT SIGN COMPARISONS
PERCENT POSITIVE
REANALYSIS
HANUSHEKa ALL GOOD BAD
TEACHER EDUCATION 46.4 67.2 66.7 67.3
TEACHER EXPERIENCE 69.1 68.8 65.2 70.7
TEACHER SALARY 66.7 59.1 59.1
OTHER TEACHER CHAR. 86.8 94.7 84.2
TEACHERS PER PUPIL 37.4 74.2 70.6 75.6
EXPENDITURE PER PUPIL 70.4 81.3 84.6 80.0
SCHOOL SIZE 45.8 71.4 37.1
TOTAL 56.1 68.8 75.2 66.7
aHanushek (1986). Excludes coefficients listed as having unknown sign.
findings.
There is generally little difference in coefficient signs between the studies I classify as good
and those I classify as bad. In aggregate, 75.2 percent of the good studies and only 66.7 percent
of the bad studies have the correct sign. Three quarters of this difference is attributable to the
school size coefficients, which are nearly twice as likely to be positive in the good studies. Other
teacher characteristics also are more commonly positive in correctly specified studies.
Thirty seven percent of the 414 coefficients are significantly positive at a 5 percent (onetail)
significance level. To facilitate comparison with Hanushek (1986), Table 33 reports the
frequency with which the coefficients are significantly positive at the 2.5 percent level with a
onetail test (or, equivalently, at the 5 percent level using a twotail test). Almost a third of my
coefficients are significantly positive, far more than the 2.5 percent that would be due to chance.
There is considerable variation in the frequency of significance. Nearly half the coefficients on
teacher experience, other teacher characteristics, and per pupil spending are significant, but only
a sixth of the coefficients for teacher education, teachers per pupil, and school size are
significant.
TABLE 33
META ANALYSIS: COEFFICIENT SIGNIFICANCE COMPARISONS
PERCENT SIGNIFICANTLY POSITIVE
REANALYSIS
HANUSHEKa ALL GOOD BAD
TEACHER EDUCATION 8.7 17.2 25.0 15.4
TEACHER EXPERIENCE 35.1 42.2 52.2 36.6
TEACHER SALARY 25.0 31.2 31.2
OTHER TEACHER CHAR. 43.4 52.6 40.4
TEACHERS PER PUPIL 9.9 17.7 17.6 17.8
EXPENDITURE PER PUPIL 24.1 48.9 30.8 56.7
SCHOOL SIZE 18.1 38.1 11.3
TOTAL 20.3 30.2 38.1 27.5
aHanushek (1986). Excludes coefficients listed as having unknown sign.
Note: significant at the 2.5 percent level using a onetail test
Once again, Hanushek's summary was less favorable to educational inputs than ours. Only
20.3 percent of his coefficients were significant. For each of the five input categories, his
coefficients were less often significant than were the coefficients in my reanalysis. The biggest
difference was for spending; his were half as likely as my coefficients to be significant. How
much of this is due to my slightly different selection and recording criteria and how much is due
to the inclusion of 18 new papers is not certain. However, the fact that only 5 of the papers
yielding data in Hanushek's survey were dropped and 18 new ones were included suggests that
the latter factor is dominant.
Specification is important to conclusions about statistical significance. Good studies were 39
percent more often significant than were bad studies. The correctly specified studies were much
more likely to find that school size and various indicators of teacher quality were significant.
Specification did not matter for conclusions about the effect of smaller class size; few good or
bad studies found that to matter. Surprisingly, spending was significant more often in bad
studies than in good studies. The meager effect of specification on sign together with the sizable
impact on significance suggests that misspecification produces insignificant results largely
through higher estimated errors.
Describing the frequency with which a variable is highly significant, called vote counting,
provides some information about the variable's statistical success but does not result in a
conclusion about its overall significance in the group of studies. Furthermore, "even when an
effect is present in every study, vote counting typically has very low power to detect effects (it is
prone to type II errors)" [Greenwald, Hedges, and Laine, (1994, p. 10)]. I followed the meta
analysis literature and used the inverse chisquare test, known also as the Fisher test or the
Pearson P) test, to assess overall significance.10 Let pi be the probability that the coefficient is,
say, less than or equal to zero (the null hypothesis). Assuming that each coefficient represents an
independent test of the null hypothesis, then it can be shown that X2logepi, i=l1, 2, ... k, has a X2
distribution with 2k degrees of freedom. This statistic will be used to test the null hypothesis that
the parameter is less than or equal to zero, based on evidence from the set of k regressions. The
nonpositive null could be rejected by many moderately significant or a few highly significant
positive coefficients. This test has been used by Kenny (1980), Greenwald, Hedges, and Laine
(1994), Hedges, Laine, and Greenwald (1994a), Hedges and Greenwald (1996), and others to
evaluate various education production function results.
One drawback of my analysis is that onetail tests such as the Fisher test can yield seemingly
inconsistent results. That is, it is possible to reject the null hypothesis that the coefficient is non
positive in all studies and also reject the null hypothesis that the coefficient is nonnegative in all
studies. Much of this is due to a small number of highly significant coefficients with the
unexpected sign. Economic theory, of course, implies that inputs always should have a positive
coefficient. To eliminate the influence of a few aberrant studies, I follow common practice in
this literature and drop the 5 percent of the results that were most significantly positive and the 5
percent of the results that were most significantly negative; 370 of the original 414 coefficients
remain. Inconsistency, not a major problem, was virtually eliminated by culling the results in
this fashion.
As noted above, the inverse chisquare test is based on the assumption that these coefficients
are independent. Since results taken from several studies that use the same sample and
dependent variable are not independent, I use the mean probability across the commondata
10 See Maddala (1977, pp. 4748) and Hedges and Olkin (1985).
studies which remain after deleting the extreme positive and negative five percent to summarize
the significance of the school input in that data set with that achievement test. Thus, only one
probability is entered for each sample and dependent variable in the calculation of the X2
statistic.11 This solution to commondata studies reduces the number of "results" from 370 to
333.
The inverse chisquare tests based on these results are reported in Table 34. Panel A gives
the evidence from both good and bad studies on the coefficient being positive, where the null
hypothesis is that the coefficient is nonpositive. The first and fourth columns indicate the
number of "results," and the second and fifth columns report the probability of accepting the null
hypothesis. It is rejected for all school input categories for the good studies and for all categories
but school size for the bad studies. Based on this test alone, there is strong evidence from both
correctly and incorrectly specified tests that school inputs boost learning.
Evidence that the coefficient is negative is reported in Panel B. The good studies accept the
null hypothesis that the coefficient is nonnegative for the coefficients as a group and for all
input categories but school size. The incorrectly specified studies reject the null for the group as
a whole and for school size and accept it for the other categories.
11 I already have mitigated this problem by using only the "best" regression for a dependent
variable and sample from any paper. I also tried using the median rather that the mean to
combine commondata studies. This did not change any of the conclusions from the analysis; in
fact the results were nearly identical. I also tried combining all results from the same sample
using different dependent variables so that each data set would yield only a single observation.
However, this left too few observations among the good studies to provide any meaningful
insight.
TEACHER EDUCATION
TEACHER EXPERIENCE
TEACHER SALARY
OTHER TEACHER CHAR.
TEACHERS PER PUPIL
EXPENDITURE PER PUPIl
SCHOOL SIZE
TOTAL
TEACHER EDUCATION
TEACHER EXPERIENCE
TEACHER SALARY
OTHER TEACHER CHAR.
TEACHERS PER PUPIL
EXPENDITURE PER PUPIl
SCHOOL SIZE
TOTAL
aThe 5 percent of the results
negative were deleted.
TABLE 34
META REANALYSIS: JOINT SIGNIFICANCE TESTS
MIDDLE 90% OF RESULTSa
A: POSITIVE CASE (Ho: B < 0)
Good Studies Bad Studies
Joint Joint
# Significance # Signific
0}) 2) (4) (5)
10 .003 41 .000
17 .000 34 .000
0 19 .000
7 .000 48 .000
15 .000 35 .000
L 11 .000 21 .000
20 .000 55 .392
80 .000 253 .000
B: NEGATIVE CASE (Ho: B > 0)
Good Studies Bad Studies
Joint Joint
# Significance. # Signific
0) 2) 2(3) 4)
10 .939 41 .563
17 .476 34 .999
0 19 .645
7 .999 48 .999
15 .839 35 .976
L 11 .997 21 .999
20 .000 55 .000
80 .178 253 .000
that were most significantly positive and the 5 percent tha
Combining the results from both panels, there is strong evidence from both good and bad
studies that each school input except school size has a positive impact on learning. The results
from the good studies do not provide consistent evidence on whether the coefficients on school
size are positive. The misspecified studies are even less favorable to the hypothesis that students
learn more in larger schools; they suggest that the true coefficient is negative.
My analysis is based on a larger literature than was summarized by Hanushek. With this
broader set of results, I find less inconsistency with the inverse chisquare test than did Hedges,
Laine, and Greenwald (1994a) in their analysis of the papers summarized by Hanushek. In my
ance
ance
were most significantly
full set of 414 regression results, there were (unreported) inconsistent results on teacher
education and school size. Hedges, Laine, and Greenwald did not summarize school size results
and report inconsistencies on teacher education, teacher salary, and the pupil/teacher ratio for the
full sample. With the independent, middle 90% set of results reported in Table 34, I find only
the school size results in the good studies to be inconsistent. Hedges, Laine, and Greenwald
using similar procedures find inconsistency for teacher salary and teacher education.
Estimating Production Functions: Sensitivity to Specification
In this section I estimate educational production functions, based on two distinct data sets, to
determine the effect on the signs and significance of school inputs due to model misspecification.
Three types of misspecificiation are considered.
Although a number of micro (student) level data sets contain reasonable proxies for the time
parents devote to their children's education, many education production function studies include
income together with these time proxies and other socioeconomic variables. With the Project
TALENT micro data set from 1960, I determine the impact of including income with no other
change in specification. Such a clean comparison generally is not possible with metaanalysis.
Since the Project TALENT data set was used in a number of studies reviewed above, revisiting
this data set has special relevance for evaluating the education production literature.
With aggregatelevel data, reasonable proxies for parents' time inputs are more difficult to
obtain. Using statelevel data for 198792, I estimate educational production functions, based on
several different school input specifications, to test for the effects of including income in the
production function regressions. I also estimate the impact of using family income instead of
parents' education, which may occur when parent's education is unavailable.
Concern over bias in the school input coefficients arises from their correlation with omitted
parental time. With the statelevel data, an instrumental variable procedure is employed to
ascertain the extent of this bias. The instrumental variable procedure is not used for the Project
TALENT data set, since it has seven measures of the quantity and quality of parental time inputs.
Some comparison of these data sets is warranted. The Project TALENT data come from a
era when there was a stronger relationship between income and school inputs, which would
create a greater misspecification problem than would be observed with recent micro data. On the
other hand, each school is represented by only seven students on average in my Project TALENT
sample, which produces some error in estimated community characteristics for the school and
thus less correlation between schoollevel income and school inputs than would otherwise be the
case. Husted and Kenny (1998) show that recent efforts to equalize education spending have
made schools less efficient; this would make it more difficult to find school inputs significant
with the modern pooled state level data set used in this study. Hanushek, Rivkin, and Taylor
(1996) claim that aggregate studies suffer from specification bias due to the omission of state
regulations and other characteristics of the state's education structure. What they fail to realize is
that this problem also plagues the many micro studies that use large multistate data sets.
The first data set is drawn from the Project TALENT data set, a stratified random sample of
all U.S. students in grades nine through twelve in 1960. I use a subsample of nearly 4300 twelfth
grade males with complete information on relevant variables. The data come from a battery of
tests the students took and from remarkably detailed questionnaires filled out by both the student
and his high school principal. The dependent variables are 1) a verbal composite (C003) that
measures information about literature, vocabulary, spelling, capitalization, punctuation, English
usage, and effective expression, and 2) a mathematics composite (C'004) that measures
information about mathematics, arithmetical reasoning, and introductory and advanced high
school math.
The quantity and quality of parents' time is measured by the number of jobs currently held by
the father (FATHER'S JOBS), time spent in the labor force by the mother in the 1950s
(MOTHER'S WORK), number of children in the family (CHILDREN), the student's birth order
(BIRTH ORDER), the father's and mother's educational attainment (FATHER'S EDUC,
MOTHER'S EDUC), and the student's race (BLACK).
Each student was asked to pick one of five categories that best described his family's income.
Since the resulting categorical data very crudely measure family income, I have instead used the
common logarithm of the summed median 1959 sexspecific earnings, for those working 5052
weeks, in the parents' detailed occupations (LOG FAMILY INC).12 To better approximate the
situation where more aggregate income data are used, I also use the school average for my
sample of the log of family income (LOG AVE FAMILY INC); since the 4252 students in my
sample come from 579 schools, these schoolbased means are based on only 7 students on
average.
Several variables cover school inputs. The impact of large schools is captured by LOG
SCHOOL SIZE, the common logarithm of the number of students in grades 912 in the school.
Average teacher experience (TEACHERS' EXPER), the fraction of teachers with a masters
degree (TEACHERS' EDUC), and average class size (CLASS SIZE) measure the quality and
quantity of teacher inputs. The tracking of students according to ability groupings (TRACKING)
is included to test whether this increases school effectiveness.13
12 If the mother did not work, the earnings of those with her educational attainment were used.
13 Note that there were serious problems with Project TALENT's measure of spending per pupil,
which is not used in this study.
TABLE 35
PROJECT TALENT PRODUCTION FUNCTION OLS REGRESSIONS
(absolute tstatistics in parentheses)
Independent
Variables
INTERCEPT
FATHER'S JOBS
MOTHER'S WORK
CHILDREN
FATHER'S EDUC
MOTHER'S EDUC
BLACK
0.016
BIRTH ORDER
LOG SCHOOL SIZE
TEACHERS' EXPER
TEACHERS' EDUC
CLASS SIZE
TRACKING
SCHOOL YEAR 181.31
SCHOOL DAY
MISSED SEMESTERS
DAYS ABSENT
HOURS STUDYING
CHANGING SCHOOLS
LOG FAMILY INC
AVE LOG FAMILY INC
Adjusted Rsquare
Root Mean Squared Error
Number of Observations
Mean
(S.D.
1.191
(0.494)
1.880
(2.769)
3.379
(1.915)
11.414
(3.159)
11.573
(2.478)
4.169
(0.063)
1.858
(1.336)
2.922
(0.426)
13.124
(4.129)
0.599
(0.276)
27.690
(3.915)
0.462
(0.262)
0.117
(4.881)
343.42
(49.20)
0.128
(0.542)
6.085
(5.381)
9.120
(5.713)
1.508
(1.681)
3.948
(0.084)
3.948
(0.042)
74.62
(6.87)
1.053
(2.01)
0.037
(0.39)
0.753
(4.36)
0.995
(9.92)
0.798
(6.34)
4.307
(1.01)
0.573
(2.35)
2.217
(2.23)
0.098
(1.43)
1.019
(0.77)
0.156
(2.00)
1.085
(0.98)
0.111
(2.00)
0.0091
(1.65)
3.261
(6.77)
0.173
(3.55)
0.617
(13.4)
0.301
(1.91)
0.1752
16.811
4252
VERBAL
A2
22.80
(1.26)
1.001
(1.92)
0.024
(0.26)
0.684
(3.98)
0.770
(7.30)
0.425
(3.10)
4.836
(1.05)
0.645
(2.65)
1.989
(2.01)
0.097
(1.42)
0.905
(0.69)
0.161
(2.08)
1.122
(1.02)
0.098
(1.90)
0.0087
(1.58)
3.201
(6.68)
0.175
(3.62)
0.605
(13.2)
0.306
(1.95)
26.94
(6.68)
0.1836
16.725
4252
145.7
(5.09)
1.001
(1.92)
0.0060
(0.06)
0.656
(3.82)
0.856
(8.48)
0.608
(4.79)
16.01
(1.18)
0.630
(2.60)
1.030
(1.03)
0.104
(1.53)
0.111
(0.08)
0.114
(1.47)
1.196
(1.09)
0.160
(1.69)
0.0079
(1.44)
3.151
(6.59)
0.180
(3.72)
0.595
(13.0)
0.403
(2.57)
58.43
(8.31)
0.1883
16.678
4252
4)
1.378
(0.06)
0.104
(0.09)
0.141
(0.68)
1.262
(3.33)
2.166
(9.82)
1.962
(7.09)
16.34
(1.76)
0.931
(1.74)
6.257
(2.87)
0.037
(0.24)
6.936
(2.39)
0.244
(1.42)
4.195
(1.73)
0.144
(1.25)
0.025
(2.07)
6.078
(5.74)
0.602
(5.63)
1.751
(17.2)
1.083
(3.13)
0.2081
36.956
4252
MATH
238.0
(5.97)
0.025
(0.02)
0.0087
(0.04)
1.095
(2.90)
1.618
(6.99)
1.057
(3.51)
17.32
(1.81)
1.105
(2.07)
5.704
(2.63)
0.033
(0.22)
6.658
(2.31)
0.257
(1.51)
4.286
(1.78)
0.123
(1.13)
0.024
(2.00)
5.932
(5.64)
0.608
(5.71)
1.723
(17.1)
1.095
(3.18)
65.42
(7.39)
0.2180
36.724
4252
(6)
434.7
(6.90)
.00074
(0.00)
0.080
(0.39)
1.072
(2.84)
1.892
(8.51)
1.589
(5.68)
(1.92)
1.042
(1.95)
3.922
(1.79)
0.048
(0.32)
5.149
(1.78)
0.161
(0.94)
4.412
(1.83)
(0.96)
0.023
(1.89)
5.861
(5.57)
0.616
(5.79)
1.708
(16.9)
1.284
(3.72)
114.9
(7.42)
0.2181
36.722
4252
As a student spends more time in class, there is an increase in both his time input and school
inputs. Class time variables used in this study include days in the school year (SCHOOL
YEAR), minutes in class in the school day (SCHOOL DAY), and selfreported data on the
number of full semesters missed (MISSED SEMESTERS) and number of days absent from
school the prior year (DAYS ABSENT). Hours spent studying each week (HOURS
STUDYING) further measures the time the student devotes to learning. If changing schools
disrupts learning, the number of times the student has changed schools since first grade
(CHANGED SCHOOLS) should have a negative impact on achievement.
Six regressions are reported in Table 35 for the two dependent variables. The first and
fourth regressions do not include any income measure. My measure of the student's family
income (LOG FAMILY INC) is included in the second and fifth regressions, and my measure of
mean family income in the school (LOG AVE FAMILY INC) is used in the third and sixth
regressions. The fits are good for micro data, and most of my hypotheses are supported.14
Family income is used in education production functions as a proxy for parental time. My
regressions include seven variables that more directly measure the quality and quantity of
parental time. If parental time in the labor force comes at the expense of time with their children,
then FATHER'S JOBS and MOTHER'S WORK should have negative coefficients. Nine of the
twelve coefficients are indeed negative, but only FATHER'S JOBS is significant, in the
VERBAL regressions. The parental time allocated to each child is expected to fall as the number
of children in the family rises, and CHILDREN has the predicted negative impact on
achievement. Children of higher birth order typically are born when their parents are older and
commanding higher wages; the negative coefficients on BIRTH ORDER suggest that children
14 The first and fourth regressions are very similar to a regression which was included in the
born later receive less help from their parents. The highly significant positive coefficients on the
parental education variables support the hypothesis that more educated parents are more effective
in teaching their children. The coefficients on BLACK are negative and are marginally
significant in the MATH regressions; AfricanAmericans may have lower test scores because
their parents attended lower quality schools. In the regressions where they are included, the two
income measures have a positive and significant impact on test scores.
Most of the hypotheses regarding school inputs are supported in the "good" regressions (1
and 4). In contrast to many educational production function studies, I find that students learn
more in larger schools, as Kenny (1982) predicted. Achievement is also found to be higher when
students are taught in smaller classes. The evidence on which aspect of teacher quality is
important is inconsistent. Students have higher verbal scores when taught by more experienced
teachers and are more proficient in mathematics when taught by more educated teachers; in the
other regression, these variables do not affect test scores. The positive and significant coefficient
on TRACKING in the MATH regression is consistent with students learning more when they are
placed in homogeneous "ability" groupings; with tracking, fewer students are lost or bored.
TRACKING is, however, insignificant in the VERBAL regression.
There is much speculation but little evidence on the efficacy of student time. The four
variables capturing student time together with school inputs generally have the predicted effects.
Achievement is higher when students spend more time each day in school; a longer school year
produces higher verbal scores but has no impact on math performance. Students who have lost a
semester or have been absent many days have lower test scores. Time spent studying at home or
in study periods is very effective. HOURS STUDYING has a positive and highly significant
analysis of the previous section.
impact on achievement. The significantly negative coefficients on CHANGED SCHOOLS
suggest that there is some adjustment cost to changing schools.
Since there are seven measures of the quality and quantity of parental time in these
regressions, there is no rationale for adding income to these regressions. I nevertheless examine
the impact of doing so. The student's family income measure (LOG FAMILY INC) is used in
the second and fifth regressions. Including family income generally makes it more difficult to
conclude that school inputs have their predicted impact. LOG SCHOOL SIZE, TEACHERS'
EXPER, TEACHERS' EDUC, SCHOOL YEAR, and SCHOOL DAY become less significant,
but the tstatistic for CLASS SIZE becomes larger. In the VERBAL regression, use of LOG
FAMILY INC leads to the rejection of the hypothesis that the school year is significant at the 2.5
percent level (with a one tail test) and makes the school day coefficient insignificant at the 5
percent level.
School inputs fare even worse when the more aggregate schoolbased measure of income
(LOG AVE FAMILY INC) is added to the specification. In the VERBAL regression, the
following important changes in one tail significance levels are observed: 1) LOG SCHOOL
SIZE: .013 to .151; 2) CLASS SIZE: .023 to .079; 3) SCHOOL YEAR: .023 to .045; 4)
SCHOOL DAY: .050 to .074. In the MATH regression, there were a number of instances where
common significance thresholds (.025, .05, .10) were passed: 1) LOG SCHOOL SIZE: .002 to
.037; 2) TEACHERS' EDUC: .008 to .038; 3) CLASS SIZE: .077 to .173; 4) SCHOOL DAY:
.019 to .029. In one exception to this pattern, TEACHERS' EXPER becomes more significant
when community income is included.
The inclusion of income often makes it more difficult to conclude that school inputs are
effective in part because it seems to bias the school input coefficients toward zero. Adding LOG
FAMILY INC lowers the coefficients on school size, teacher experience, teacher education,
school year, and school day by 7 percent on average and raises the coefficients on class size
slightly. Adding instead the more aggregate income measure LOG AVE FAMILY INC, which
is more correlated with school inputs, reduces the LOG SCHOOL SIZE, TEACHERS' EDUC,
CLASS SIZE, SCHOOL YEAR, and SCHOOL DAY coefficients by an average of 33 percent
but raise the TEACHERS' EXPER coefficients.
The second production function I estimate is based on pooled statewide data, which have less
measurement error than is often found in educational production function studies. Since there is
much less mobility of students across states than across school districts or schools, the state
educational characteristics more closely approximate the students' educational experiences than
do current district or school educational measures. On the other hand, having better educational
measures would be of little value if student and parental inputs were more poorly measured. In
contrast to many other statewide studies, I have good information on the testtakers and their
families.
Using ordinary least squares (OLS), I first estimate several specifications of the simple
education production function. My educational output measure in each is the average state total
verbal and math SAT score. These test scores as well as several of my independent input
variables are obtained from Educational Testing Service (ETS) reports on 37 states over 6 years.
ETS did not publish reports on testtakers from the other 13 states due to the small numbers and
percentages of students who took the SAT examinations in each year.15 With the ETS reports, I
are able to utilize the characteristics of the testtakers and their families instead of the
15 Since the thirteen omitted states  Idaho, Iowa, Kansas, Kentucky, Louisiana, Mississippi,
Montana, Nebraska, North Carolina, North Dakota, South Dakota, Utah, and Wyoming  have a
wide range of average SAT scores, omitting these states from my analysis is unlikely to be a
characteristics of the general state population, found in many statewide studies.16 Obviously,
statewide characteristics do not always correspond with the characteristics of the state's test
takers. With testtaker data, I can better estimate the impact of family inputs and student
characteristics on achievement. My sample of 222 observations starts in 1987, the first year for
which parental educational attainment was reported by ETS, and ends in 1992. To complete the
basic specification, I combine these testtaker characteristics with statelevel measures of public
school characteristics. The summary statistics for the independent variables from these models
are reported in Table 36.
TABLE 36
SUMMARY STATISTICS FOR STATE PRODUCTION FUNCTION VARIABLES
INDEPENDENT VARIABLE MEAN STANDARD
DEVIATION
PARENTS' EDUCATION 4.0519 0.1600
BLACK 1.5982 0.9687
FAMILY INCOME GINI 1.2142 0.0452
PUBLIC 4.3612 0.1035
ENGLISH 4.3886 0.0500
MATH 4.0994 0.1136
LARGE SCHOOL 1.5259 2.2927
PUPILS PER TEACHER 2.8254 0.1195
TEACHERS' EXPERIENCE 3.6919 0.1461
TEACHERS' EDUCATION 3.8569 0.2374
TEACHERS' REL WAGE 9.7780 0.1177
SPENDING PER PUPIL 8.2086 0.2242
REAL PER CAPITAL INCOME 9.5375 0.1483
PARTICIPATION 3.4771 0.7600
In the first set of OLS regressions, I examine the basic forms of model misspecification. The
first type that I consider arises when important family characteristics are unavailable and family
problem.
16 Powell and Steelman (1984) and Graham and Husted (1993) also use data on the testtakers.
income, usually some measure of state income, is substituted as a proxy measure for these
missing characteristics. This form of misspecification is most prevalent when aggregate data like
these are used to estimate the educational production functions. Because the ETS data include a
measure of parent's education, it is possible to estimate the effects of this misspecification.
I measure parents' education by the fraction of testtakers' parents with an Associate's Degree
or higher (PARENT'S EDUCATION). I use as my measure of income real state per capital
personal income in 198284 dollars (REAL PER CAPITA INCOME). In addition to these
variables, I incorporate other family characteristics taken from the ETS data set. To allow for
any historical inferiority of resources devoted to black education, I include the fraction of test
takers who are black (BLACK). Since educational systems often address the needs of the typical
student, teaching may be less effective in states with more heterogeneous pupils. I test this
hypothesis with a Gini coefficient of testtaker family income inequality (FAMILY INCOME
GINI), which is calculated from the reported grouped data on income.
To capture the students' exposure to the major SAT subjects, I include the fractions of test
takers that took four or more classes in English (ENGLISH) and math (MATH). I test the
hypothesis that students in large schools learn more with the variable LARGE SCHOOL, which
equals the percentage of testtakers who attend a school with 500 or more students in the senior
class.
Public schools are much more regulated than private schools and should be less efficient than
private schools if the regulations impose constraints on the production process. Public schools
also may lose some of their best students to private schools. A number of studies, most notably
Coleman, Hoffer, and Kilgore (1982), have found that public school students have lower test
scores than do private school students. My variable PUBLIC equals the fraction of testtakers
that attend public school.
A number of general public school characteristics are taken from the annual issues of the
Digest of Educational Statistics. The quantity of teaching inputs devoted to each student is given
by the student/teacher ratio in the state's schools (PUPILS PER TEACHER).17 Teacher quality
is captured alternatively by 1) the fraction of teachers with 10 or more years of teaching
experience (TEACHERS' EXPERIENCE) and the fraction of teachers with at least a Master's
degree (TEACHERS' EDUCATION), or 2) the ratio of teacher salaries to average earnings in the
state (TEACHERS' REL WAGE). The latter measure follows Card and Krueger (1992), who
normalize state teacher wages by the average earnings of all employees in the state covered by
the social security system to control for geographic differences in cost of living, amenities, and
in statespecific opportunity costs of teaching. Finally, SPENDING PER PUPIL in 19824
dollars is used as a summary measure of school inputs.
Although often reported as performance measures of state school systems, average state SAT
scores contain a potential bias. States in which a greater share of high school students go on to
college, and thus take SAT or ACT tests, draw students from further down the distribution of
skills, pulling down average test scores. Moreover, if a state's universities do not require the
SAT for admission and instead require the ACT or some other test, few take the SAT test and
many who do take it are applying to outofstate universities. Since admission to outofstate
universities is often more selective, this effect also would cause the average SAT scores in the
state to be higher in states with low participation rates.
17 Pupils per teacher measures class size with error, due to differences across districts in
preparation periods, the use of teachers in nonteaching functions, etc.
Several recent empirical studies attempt to correct this potential bias by including a measure
of state participation rates directly in the regressions. Dynarski (1987) includes the state
participation rate in his empirical educational production function. Behrendt, Eisenach, and
Johnson (1986) and Graham and Husted (1993) develop an alternate model of selection that
yields a specific functional form of the relationship between participation and state SAT scores.18
In all cases, the state test taking participation rate has a significantly negative impact on
statewide average examination scores. My measure (PARTICIPATION) is the number of test
takers divided by the number of public and private high school graduates.19
Table 37 reports the results of nine OLS regressions. Each of the nine regressions uses the
state average SAT score as the dependent variable and includes a common set of explanatory
variables. All variables are measured in logarithms. Each of three sets of regressions has a
common form. Using the previous terminology, the specification of the first regression in each
set [regressions (1), (4), and (7)] is considered to be "good." That is, PARENTS' EDUCATION
is included and REAL PER CAPITA INCOME is excluded. The other two regressions in each
set introduce misspecification. The second regression [(2), (5), and (8)] includes both
PARENTS' EDUCATION and REAL PER CAPITAL INCOME. Finally, in order to gauge the
impact of the most egregious form of model misspecification on the various school input
variables, REAL PER CAPITAL INCOME replaces PARENTS' EDUCATION in the third
regression in each set [(3), (6), and (9)]. The regressions also differ by the included public
school input measures. In the first six regressions, school inputs are captured by teacher quantity
(PUPILS PER TEACHER) and the three measures of teacher quality described above. Teacher
18 The specific details are outlined in Behrendt, Eisenach, and Johnson (1986).
19 My correction, like others in this literature, adjusts for selection in the group of high school
seniors in taking the SAT test but does not deal with those who dropped out earlier.
skills are measured in the first three regressions by teacher education and experience
(TEACHERS' EXPERIENCE, TEACHERS' EDUCATION) and in second three regressions by
the relative salary of teachers (TEACHERS' REL WAGE). In regressions (7)(9), SPENDING
PER PUPIL is the only school input variable. In all nine OLS regressions, I get a very good fit
and most of my hypotheses are supported.20
In the six regressions where they are included, PARENTS' EDUCATION has the expected
positive and statistically significant effect on student achievement. In all of the specifications,
average test scores are lower in states with more black testtakers. In part, this result may be
because black testtakers or their parents went through worse schools than whites. It also may
reflect the generally lower quality of education in many southern states with large black
populations. In addition, REAL PER CAPITA INCOME has significantly positive coefficients,
consistent with its role as a proxy for parental inputs.
An increase in the Gini coefficient on the family incomes of testtakers (FAMILY INCOME
GINI) is associated with greater income inequality. The negative and significant coefficients
estimated on FAMILY INCOME GINI in all of the regressions support my hypothesis that the
educational system is less efficient when the student body comes from a more diverse
background.
The estimated coefficient on PUBLIC is negative and significant in eight of the nine models.
I, like others, find that public school students have lower test scores than private school students.
This may reflect the relative inefficiency of the public schools or a sorting of the better students
into private school. The coefficients on the fractions of testtakers that have had four or more
20 Again, the first regression here was included in the analysis of section one.
English courses (ENGLISH) or math courses (MATH), on the other hand, vary in sign and
significance.
INDEPENDENT
VARIABLE
INTERCEPT
PARENTS'
EDUCATION
BLACK
FAMILY
INCOME GINI
PUBLIC
ENGLISH
MATH
LARGE SCHOOL
PUPILS PER
TEACHER
TEACHERS'
EXPERIENCE
TEACHERS'
EDUCATION
TEACHERS'
REL WAGE
SPENDING
PER PUPIL
REAL PER
CAPITAL INCOME
PARTICIPATION
Adjusted R2
Observations
TABLE 37
STATE POOLED PRODUCTION FUNCTION OLS REGRESSIONS
Coefficient Estimates
(absolute value of tstatistics)
(1) (2) (3) (4) (5) (6) (7) (8) (9)
6.987 5.951 5.829 7.075 6.181 5.905 6.257 5.974 5.965
(44.4) (31.6) (22.7) (49.2) (32.5) (22.7) (43.6) (33.6) (24.6)
0.200 0.135  0.200 0.163  0.160 0.149 
(17.2) (7.98) (17.5) (13.8) (15.5) (13.5)
0.010 0.012 0.014 0.009 0.010 0.013 0.010 0.010 0.012
(8.32) (10.7) (9.48) (7.63) (9.21) (8.83) (9.20) (9.59) (8.88)
0.116 0.080 0.072 0.113 0.095 0.090 0.106 0.097 0.088
(4.74) (3.67) (2.44) (4.60) (4.16) (2.89) (4.83) (4.43) (2.97)
0.072 0.039 0.026 0.073 0.041 0.015 0.078 0.061 0.037
(6.58) (3.74) (1.84) (6.91) (3.75) (1.04) (8.11) (5.30) (2.35)
0.066 0.033 0.055 0.037 0.002 0.002 0.018 0.023 0.023
(2.36) (1.31) (1.63) (1.41) (0.07) (0.05) (0.75) (0.97) (0.70)
0.011 0.009 0.046 0.026 0.007 0.032 0.008 0.012 0.030
(0.87) (0.84) (3.07) (2.06) (0.60) (2.00) (0.75) (1.12) (2.09)
0.0022 0.0012 0.0007 0.0024 0.0014 0.0004 0.0021 0.0015 0.0011
(4.29) (2.55) (1.02) (4.77) (2.84) (0.56) (4.56) (3.15) (1.64)
0.056 0.033 0.0114 0.075 0.054 0.007   
(5.51) (3.53) (0.96) (7.23) (5.41) (0.56)
0.018 0.030 0.0488      
(2.31) (4.31) (5.20)
0.0084 0.0077 .0030      
(1.80) (1.88) (0.56)
0.040 0.017 0.008 
(2.62) (1.21) (0.43)
      0.053 0.041 0.030
(10.2) (6.05) (3.29)
 0.079 0.141
(8.09) (12.0)
 0.067 0.134 
(6.51) (10.7)
0.033 0.100
(2.63) (6.25)
0.031 0.046 0.077 0.033 0.045 0.078 0.040 0.044 0.08
(12.0) (15.7) (31.7) (12.5) (14.8) (30.1) (15.9) (14.8) (31.6)
0.934 0.950 0.907
0.934 0.945 0.895 0.945 0.946 0.900
222 222 222 222 222 222 222 222 222
PARTICIPATION controls for differences among states in the fraction of seniors who take
the SAT tests. My results are consistent with other research, which finds that SAT scores fall as
a larger fraction of the state's high school students take the test.
The focus of my research is on the impact of this specific type of model misspecification on
the various school input variables. In my "good" models [regressions (1), (4), and (7)], there is
strong evidence that school inputs matter to student achievement. In regression (1),
TEACHERS' EXPERIENCE and TEACHERS' EDUCATION have statistically significant
positive impacts on SAT scores. The coefficient on TEACHERS' REL WAGE in regression (4)
is positive and significant as well. In both these regressions, SAT scores are significantly lower
in states with more pupils per teacher. SPENDING PER PUPIL, the summary school input
measure, has a highly significant positive impact on learning in (7). The positive and significant
coefficients estimated on LARGE SCHOOL support Kenny's (1982) prediction that schools
operate in a region of increasing returns to scale.
The regressions summarized in the remaining columns illustrate the statistical problems that
result when family income serves its dubious role as a proxy for family inputs. Including income
in these education production functions causes four school variables to become less significant
and one variable (TEACHERS' REL WAGE) to lose significance. Replacing parents' education
with average income has a devastating impact, with four school measures (LARGE SCHOOL,
PUPILS PER TEACHER, TEACHERS' EDUCATION, and TEACHERS' REL WAGE)
becoming insignificant, three of these even changing sign! The only public school input that
does not do worse when income is included is teachers' experience. Contrary to expectations,
the positive coefficients on TEACHERS' EXPERIENCE become slightly more significant when
income is included in regressions (2) and (3). The evidence strongly suggests that the inclusion
of income biases the school input coefficients toward zero. Only the TEACHERS'
EXPERIENCE coefficients become larger, and the coefficients of the other five school measures
fall by 32 percent on average when income is included. Replacing education with income biases
the coefficients even more toward zero; those coefficients that retained their sign fell by 65
percent on average.
As described in the Introduction, one problem with using OLS to estimate these educational
production functions if parental time or other inputs are not included in the regressions is that the
school inputs may be correlated with the omitted inputs and thus with the regression residuals.
An instrumental variable procedure offers one solution to the bias that may result in the school
input coefficients.
I use separate regressions, corresponding to the school input demand functions D3, to create
instruments for the five public school input measures  PUPILS PER TEACHER, TEACHERS'
EXPERIENCE, TEACHERS' EDUCATION, TEACHERS' REL WAGE, and SPENDING PER
PUPIL. I use a common set of demographic and political characteristics of the state population
as determinants of the levels of these five educational inputs.21 To capture income effects, I
include the measure of real per capital state personal income (REAL PER CAPITA INCOME)
that I used in the OLS regressions and the spread of income in the state. INCOME SPREAD
equals the difference between the first and third quartile family incomes divided by the median
family income. Since the political parties represent different segments of the income
distribution, I include a measure of which party controls state government. DEMOCRATIC
CONTROL equals one (negative one) if the Democrats (Republicans) control both the legislative
and executive bodies and equals zero if the two political parties share control of state
21 Poterba (1997) included many of these same variables in his model of the determinants of
government. Other socioeconomic variables that I include to reflect differences in demand for
education are the percentages of the state's population who are black (PERCENT BLACK), aged
65 years and older (PERCENT ELDERLY), live in metropolitan areas (PERCENT
METROPOLITAN), and have a college education (PERCENT COLLEGE). The percent of the
state's population who own their homes (PERCENT OWNER) is included to capture the
expected differences in tastes for education between owners and renters as well as to reflect the
prevalence of the ability to itemize some costs of home ownership on federal (and some state)
income taxes.
The coefficient estimates from the instrumental variable regressions are reported in Tables 8
and 9. The results from the regressions used to create the five public school input instrumental
variables are reported in Table 38. These regressions explain between 18 and 61 percent of the
variation in the five school input measures.
REAL PER CAPITA INCOME is the most consistently significant variable in these
regressions. Its importance in explaining school inputs points to the potential econometric
problems of incorrectly including income in a production function equation with these school
inputs. The hypothesized demand relationships between income and the school inputs are mostly
supported. As expected, holding other state demographic and political variables constant, higher
state per capital income leads to lower pupilteacher ratios, a higher proportion of more
experienced and higher educated teachers, and larger real per pupil education spending. The
only unexpected finding was the inverse relationship between state per capital income and the
teacher's relative wage.
government education spending.
