Transparency, Performance, and Agency Budgets:
A Rational Expectations Modeling Approach
Rosen Valchev
Antony Davies
Kevin Shaver
April 11, 2011
1
The goal of this paper is two-fold:
1. To develop a theoretical model that describes interactions of
a. A government agency that seeks to maximize its budget by
allocating energy to improving performance versus altering
the transparency of information about its performance
b. A committee of politicians who award the agency’s budget
based on the agency’s social benefit, who determine the
relevance of the agency’s revealed information, and who
observe the agency with individual biases and errors.
2. To fit the model to performance data from the Performance
and Accountability Reports (PAR) and transparency and
relevance data from Scorecard.
2
Let an agency’s budget reflect the social benefit the agency
provides. Let the budget be a positive function of the quality of the
agency’s service (the agency’s “performance”) (Gilmour and Lewis,
2006).
Assuming for the moment that the agency’s performance, p, is
observed, we have:
Budget  Social Benefit  B  p 
dB
d 2B
p  0,
 0,
0
2
dp
dp
3
The politicians.
4
Politicians don’t get to observe p. Instead, each forms an
individual perception of the agency’s performance.
pˆ i  politician i's perception of
the agency's performance
Each politician’s performance perception deviates from the
agency’s true performance due to the politician’s bias,ф, and
idiosyncratic error, є.
pˆ i  p  i   i , E  i   0
5
N politicians form a committee that control’s the agency’s budget.
pˆ  committee's perception of the agency's performance
1
pˆ   pˆ i
N i
1
pˆ  p   i   i 
N i
Unbiasedness assumption: E i   0
6
The unbiasedness assumption allows the committee to view the
agency as a lottery wherein the expected outcome is the social
benefit, B(p).
The relationship between the expected outcome and the
committee’s expected performance is (Varian, 1992):
2
d
1 B  p
B  p   B  p  p  pˆ 
2 dp 2
2
d
1 B  p
 B  p ˆ 
p p
2 dp 2
E  pˆ  p 
2
p  pˆ
var i   i 
p  pˆ
Disagreement among politicians
as to the agency’s performance.
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The agency.
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The agency self-reports performance p .
The self-reported performance can be more or less transparent, T.
Transparency can reduce disagreement.
d var i   i 
dT
 0, T  0
Politician i can perceive the self-reported performance to be more
or less relevant, ri .
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A politician’s perception of the relevance of the self-reported
performance is influenced by:
• Confirmation bias: The better is the politician’s a priori
perception of the agency’s performance, the greater the
relevance the politician will perceive (Wason, 1960).
dri
0
dpˆ i
• Honesty bias: Politicians perceive self-reported performances
that identify weaknesses as more credible (Pechman and
Estaban, 1994).
dri
0
dp
10
dri
0
dpˆ i
pˆ i
ri  c , c  0
p
dri
0
dp
1
N
r  c
i
i
1
N
 pˆ
i
i
p
pˆ
 r c
p
pr
pˆ 
c
11
B  p   B  p  p  pˆ 
2
1 d B  p
2
dp
pr
pˆ 
c
var i   i 
2
p  pˆ
B  p   B  p  p  pr
c
2
d
1 B  p

2 dp 2
var i   i 
p
pr
c
12
B  p   B  p  p  pr
c
2
d
1 B  p

2 dp 2
var i   i 
p
pr
c
dB  p 
dT

2
1 d B  p
2
dp 2
d var i   i 
p
pr
c
dT
dB  p 
B  p   B  p  p  pr 
c
dT
d var i   i 
var i   i 
dT
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dB(p) / dp is positive
(Gilmour and Lewis 2006)
Positive when p > p*, negative when p < p*
(Banks 1990, Kouzmin 1999)
dB  p 
B  p   B  p  p  pr 
c
dT
d var i   i 
var i   i 
dT
Positive (by definition)
Negative (by assumption)
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The data.
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Panel
22 Federal agencies from 2002 through 2007 (annual).
Performance data
Performance and Accountability Reports (PAR). Agency selfevaluates self-identified goals as “Not met”, “Met”, “Exceeded”.
Transparency and relevance data
Scorecard (Mercatus Center). How well agencies disclose their
performances (1=inadequate to 5=outstanding). How relevant is
performance measure (1=inadequate to 5=outstanding).
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Variable
Description
B jt
Growth rate, from year t-1 to year t, of agency j’s real discretionary
budget.
p jt
Agency j’s self-reported performance index in year t.
rjt
Scorecard’s relevance index for agency j in year t.
T jt
Scorecard’s transparency index for agency j in year t.
Gt
Growth rate of real GDP from year t-1 to year t.
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B  p   B  p  p  pr 
c
var i   i  dB  p 
d var i   i 
dT
dT
B jt  0  1Gt   2 p jt rjt  3T jt  p jt rjt  p*   u jt
B jt  0  1Gt  2 p jt rjt  3Tjt p jt rjt  3 p*Tjt  u jt
H0 :  2  0
H 0 : 3  0
H 0 : p*  0
H A :  2  0 H A :  3  0 H A : p*  0
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Table 1. Results
B jt  0  1Gt  2 p jt rjt  3Tjt p jt rjt  3 p*Tjt  u jt
Regressor
constant
Estimate
-0.084
-0.032
Standard Error
0.049
0.008
p-value
0.094
0.000
0.058
0.017
0.001
T jt p jt rjt
-0.017
0.006
0.005
T jt
0.053
0.022
0.016
Gt
p jt rjt
R2
0.23
D.W.
1.79
Feasible GLS, 22 agencies, 2003-2007, 81 observations.
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Who Cares?
We construct a behavioral model in which the agency can allocate
effort to improving performance or improving transparency and
influencing the perceived relevance of self-reported performance.
We use as a basis for the model rational expectations and lottery
models and derive a general form for the agency’s objective
function.
We then fit this model to data on performance, transparency, and
relevance and obtain results that are consistent with the model’s
prediction.
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Transparency, Performance, and Agency Budgets:
A Rational Expectations Modeling Approach
Rosen Valchev
Antony Davies
Kevin Shaver
April 11, 2011
21