Government policy and the minimization of the social loss function
Nissim Ben David
Abstract
The social loss function used in the paper is quadratic in deviations of actual from
optimal values of the objectives. In order to activate an optimal policy suggested in
this paper, the planner should estimate an econometric system of equations that relate
between the values of exogenous policy variables and targeted endogenous variables.
Minimizing social loss, subject to estimated equations constraints, the policy planner
can determine the optimal level of policy exogenous variables.
Assuming a policy planner in the U.S. is trying to minimize social damage, I
estimated the optimal policy of relevant exogenous variables, according to the
suggested model.
Key Words: Government policy; social loss function
Ben-David Nissim, Department of Economics and Management, Emek Yezreel
Academic College, 19300 Emek Yezreel, Israel. Email: NissimB@yvc.ac.il Phone
972-4-6398847, Fax 972-4-6291452
1
I. Introduction
The recent literature has seen a growth of interest in the interactions between fiscal
and monetary policies, after a long period in which each had been analyzed in
isolation as if there was only one policymaker who was able to act alone and in
his/her own self-interest. The idea that policies might interact is an old one, going
back to Tinbergen (1954), Mundell (1962) and Cooper (1969), as well as a recent one,
for example, Dixit and Lambertini (2003), Persson et al. (2006), Hughes Hallett et al.
(2005).
Monetary policies cannot be committed if fiscal policies are not committed at the
same time. However, the public must be aware that they are committed. This can be
achieved through monitoring, or because the institutional structure locks the
policymakers (see Hughes Hallett and Weymark (2007)).
The literature on discretion and commitment since the works of Kydland and
Prescott (1977) and Barro and Gordon (1983) assumes that policymakers have
preferences over inflation and employment that correspond to a quadratic loss
function.
How do and should authorities minimize the loss function? Most of the literature
discusses this in terms of a commitment to a simple reaction function, a simple
“instrument rule”, where the central bank mechanically sets its instrument rate
(usually a short interest rate like a one or two-week repurchase rate) as a given simple
function of a small subset of the information available to the central bank. Although
several different simple instrument rules have been discussed since the 1970s, the best
known and most discussed is the Taylor (1993) rule, where the interest rate is
2
determined as a function of the gap between actual and optimal rate of inflation and
the gap between actual and potential output. A large volume of research, for instance
in Taylor (1999), has examined the properties of the Taylor (1993) rule and its
variants in different models, with respect to determinacy of equilibria, performance
measured by social loss, robustness of different models, etc. Several papers have also
estimated empirical reaction functions of this type.
Inflation targeting obviously involves an attempt to minimize deviations
from the explicit inflation target. Whereas there may previously have been some
controversy about whether inflation targeting involves concern about output gap
variability, there is agreement in the literature that this is indeed the case, for instance,
Fischer (1996), King (1996), Taylor (1996) and Svensson (1996) in Federal Reserve
Bank of Kansas City (1996) all discuss inflation targeting with reference to a loss
function.
In practice, no central bank follows an instrument rule, either explicit or implicit.
Every central bank uses more information than the suggested simple rules rely on,
especially in open economies. In particular, no central bank responds in a prescribed
mechanical way to a prescribed information set. As is known by every
student of modern central banking, the bank's Board or Monetary Policy
Committee reconsiders its monetary policy decisions more or less from scratch
at frequent intervals, by taking all the relevant information into account. The bank
frequently reconsiders (and, at best, re-optimizes); once and for all, and then simply
applies the resulting reaction function forever after. This reconsideration of the bank's
decisions means that the situation is best described as decision-making under
3
discretion rather than commitment; there will inevitably be reconsiderations and new
decisions in the future, and, in practice, there is no commitment mechanism for
preventing this.
Therefore, the role of simple or complex instrument rules is, in practice, never
to commit the banks. Instead, they serve as base-lines, that is, as comparisons
and frames of reference, for the actual policy and its evaluation. In contrast,
targeting rules have the potential to serve as a kind of commitment (namely a
commitment to a loss function, although it is still minimized under discretion), and
are potentially closer to the actual practice and decision framework of (at least)
inflation targeting central banks.
Under such policy circumstances, with the banks and fiscal authorities not committed
to instrument rules, actual policy achievement should be compared to potential
achievements, given that authorities would have been committed. Such a comparison
can be made by calculating deviations from targets under discretion (actual
deviations) and under commitment.
In this paper, I present a model with a policy planner that tries to minimize a social loss
function. The social loss is determined as a sum of square deviations of actual from
optimal levels of targeted economic variables. In the first step, by using historical data,
the social planner estimates a simultaneous system of equations that connect between
endogenous (target) and exogenous (instrument) variables1. In the second step, the
planner minimizes the social loss function subject to the constraints determined by the
1
What the literature has done instead is to obtain a set of equilibrium constraints which comes from
theory.
4
simultaneous estimated equations. The optimization creates a set of equations that
determine the optimal level of the exogenous variables (instruments).
Given actual and optimal levels of the exogenous variables, the optimal and actual
social loss are calculated. In each time period ,the gap between actual and optimal loss
is calculated. The results point into times with bad economic policy and times with
good economic policy.
This paper is organized in the following manner: The model structure and an example
are laid down in section II. Estimation of the model by using U.S. data is presented in
Section III, and Section IV presents the summary.
II. The model
Let us assume that a social planner is trying to minimize social loss function by taking
k
optimal policy measures. The social loss function is of the form: Min
 (Y
i 1
i
 Yi ) 2
*
*
, where Yi is the optimal value of economic variable i, while Yi is its actual value. Yi
might be a macro economic variable such as inflation level, unemployment rate,
production rate of growth etc.
The planner can use N different economic policy measures, where X l
l  1,2...., N
is the amount of policy measure he can take. Notice that X l might be the quantity of
money, or amount of government expenditure etc.
5
.
There is a connection between policy measures taken and the value of targeted
economic variables as well as simultaneous connections between the levels of the
economic targets as presented by equation (1).
(1)
Yi  f (Y j ,Y j 1 ..., Yk ..., X 1 , X 2 .... X N )
i  1,2,....k , j  1,2,... and i  j
Assuming a linear connection, we can define (1) as:
(1a)
N
k
l 1
j 1
Yi   ail X l   bijY j
i j
 i
i  1,2,....k
If we can estimate (1a) as a simultaneous system of equations (by using a proper data
set) and identify all k equations, each of the Yi variables can be defined as a function
of the Xi exogenous variables.
We would get:
(1b)
Yi  F (ail , bij , X l , ei )
i  1,2,....k ,
l  1,2,...N ,
j  1,2,....k
Where ei is estimation error.
The planner problem can be defined as:
k
(2)
Min
X1 , X 2 ... X N
 (Y  Y
i 1
s.tYi  F (ail , bij , X l , ei )
i
i
* 2
)
i  1,2,....k ,
l  1,2,...N ,
We should notice that estimation errors are included at the constraints and will affect
policy instruments levels.
Substituting the constraint into the minimization function we get:
6
j  1,2,....k
k
( 2a )
 ( F (a
Min
X 1 , X 2 ... X
i 1
N
, bij , X l , ei )  Yi ) 2
*
il
Differentiating (2a) in respect to Xi and equalizing to zero we get:
X l  G (ail , bij , ei )
(3)
i  1,2,....k ,
l  1,2,...N ,
j  1,2,....k
Example
Let us assume that the social planner is trying to optimize the levels of two economic
variables Y1 and Y2. Their optimal value is Y1* and Y2* , while the planners' loss
(Y1  Y1 ) 2  (Y2  Y2 ) 2 .
*
function is: (4)
*
The following equations define the connection between policy measures and policy
targets:
Y1   12Y2  11 X 1   1
( 4a )
Y2   21Y1   22 X 2   2
(We should notice that given a data set of Y1t, Y2t, X1t and X2t these two equations
can be estimated as a simultaneous system with exact identification).
The planner problem is:
(4b)
(Y1  Y1 ) 2  (Y2  Y2 ) 2
*
Min
^
s.t
*
^
Y1   12 Y2  11 X 1  e1
^
^
Y2   21 Y1   22 X 2  e2
Using (4a) we isolate Y1 and Y2 and get:
^
'
( 4a )
 11
^
^
^
 12  22
 12
1
Y1  (
)X1  (
)X 2  (
)e1  (
)e 2
^
^
^
^
^
^
^
^
1   12  21
1   12  21
1   12  21
1   12  21
^
^
 21  11
Y2  (
)X1  (
^
^
1   12  21
^
^
^
^
^
^
^
 21  12  22   22   22  12  21
^
^
1   12  21
Defining
7
^
 21
)X 2  (
)e1  (
^
^
1   12  21
^
^
^
^
 21  12  1   12  21
^
^
1   12  21
)e1
^
^
 11
^
^
1   12  21
^
 A11 ,
^
^
1   12  21
 A21 ,
^
^
^
1   12  21
^
 21  11
^
^
 12  22
^
^
1
 A12 ,
^
^
1   12  21
^
^
^
 A13 ,
^
^
1   12  21
^
1   12  21
^
 21  12  22   22   22  12  21
^
 12
 A14
^
^
 21
 A22 ,
^
^
1   12  21
 A23 ,
^
^
^
 21  12  1   12  21
^
^
1   12  21
 A24
We get:
Y1  A11 X 1  A12 X 2  A13e1  A14 e2
(4a '' )
Y2  A21 X 1  A22 X 2  A23e1  A24 e2
Substituting (4a '' ) into ( 4) , we get:
(4 ' )
Min
X1 , X 2
( A11 X 1  A12 X 2  A13e1  A14 e2  Y1 ) 2  ( A21 X 1  A22 X 2  A23e1  A24 e2  Y2 ) 2
*
*
Differentiating (4' ) in respect to X1 and X2 we get:
(a)

*
*
 2 A11 ( A11 X 1  A12 X 2  A13 e1  A14 e2  Y1 )  2 A21 ( A21 X 1  A22 X 2  A23 e1  A24 e2  Y2 )  0
X 1

*
*
 2 A12 ( A11 X 1  A12 X 2  A13 e1  A14 e2  Y1 )  2 A22 ( A21 X 1  A22 X 2  A23 e1  A24 e2  Y2 )  0
X 2
Isolating X1 and X2 from (a) and (b) we get X1 and X2 as function of the A's
(b)
*
*
parameters and of e1, e2, Y1 and Y2 .
III. Optimal levels of inflation, unemployment and trade balance deficit in the U.S.
Let us assume that policy planners in the U.S. are trying to achieve a certain optimal
decrease in inflation rate, unemployment rate, and trade balance deficit.
The optimal target can be defined by D(dcpi) * - targeted decrease of inflation rate,
D(unemp) * - targeted decrease of unemployment rate and D(netexpor ts) * - targeted
decrease in trade of balance deficit.
The planner problem is:
(5)
Min
(D(dcpi)  D(dcpi) * ) 2  (D(unemp)  D(unemp) * ) 2  (D(netexpor ts)  D(netexpor ts) * ) 2
8
Estimation of constraints
First, we should estimate a simultaneous system of equations that would define the
connections between the above endogenous variables and exogenous economic policy
measures. The exogenous variables are controlled by the planner and we assume them
to be Dprime - the rate of change of prime interest rate, Dgovexp – rate of change in
government expenses, Dgovreceipt – rate of change in government receipts, Dm2
- the rate of change in M2 stock of money and D1, D2 and D3 - quarterly dummy
variables.
Data
I used U.S. quarterly data for the period 1990.1-2008.3 of the consumer price index,
government expenses, government receipts, M2 – money supply, net exports, net
government savings, prime rate and unemployment rate2.
First, in Table 1 we examine the stationarity of various series by applying the
Augmented Dickey-Fuller Test.
2
Sources of data are: U.S. Census Bureau, Bureau of Economic Analysis, Bureau of Labor Statistics:
U.S. Department of Labor and Board of Governors of the Federal Reserve System. Some data were
originally published as monthly series and were transformed into quarterly series.
9
Table 1
Augmented Dickey-Fuller Test
Null Hypothesis: variable has a unit
root
Augmented
DickeyProb.*
Fuller
test
statistic
D(dcpi) - (change in rate of inflation)
-10.29375
0.0000 -3.522887
-2.901779
Dgovexp - (rate of change in
government expenditure)
Dgovreceipt - (rate of change in
government receipts)
Dm2 - (Rate of change in M2 money
supply)
D(dm2) - (Rate of change in of change
in M2 money supply)
D(netexports) - (Rate of change in net
exports)
Dnetgovsave - (rate of change in net
government savings)
Dprime - (rate of change in prime rate)
-6.760044
0.0380 -3.522887
-2.901779
-4.124214
0.0017 -3.522887
-2.901779
-2.046790
0.2667 -3.522887
-2.901779
-10.74021
0.0001 -3.522887
-2.901779
-7.176561
0.0000 -3.522887
-2.901779
-8.266743
0.0000 -3.522887
-2.901779
-3.591650
0.0082 -3.522887
-2.901779
D(unemp) - (Change in unemployment -3.648787
rate)
*MacKinnon (1996) one-sided p-values
0.0070 -3.522887
-2.901779
10
Test
critical
values:
1% level
Test
critical
values:
5% level
The only non-stationary series is Dm2. I replaced it by using the difference series
D(dm2), which is stationary.
Several simultaneous versions were estimated by using the following instrumental
variables: d(dm2) , Dprime , Dgovexp, Dgovreceip t , Dnetgovsav e , d1, d2 , d3 .
After removing non-significant variables, I arrived at the following system of forecasted
equations (see regression results in appendix 1).
^
(5a)
d(dcpi)  0.124585 * dgovexp - 0.480559 * d3
^
d(unemp )  -0.019625dprime
^
dnetexport  -30.11515 * d(unemp)  13.39481 * d2
As we can see, there is no simultaneous relations between d(dcpi) – the change in
inflation rate and d(unemp) – the change in unemployment rate. The change in net
export (dnetexport) is negatively effected by the change in unemployment rate.
The endogenous variables are effected only by dgovexp and dprime, which are
determined by the policy planner.
At this stage, the planner should minimize the social damage subject to estimated
constraints. The planner problem becomes:
(5 ' )
s.t
Min
(D(dcpi)  D(dcpi) * ) 2  (D(unemp)  D(unemp) * ) 2  (D(netexpor ts)  D(netexpor ts) * ) 2
(6a)
d(dcpi)  0.124585 * dgovexp - 0.480559 * d3  e1
(6b)
d(unemp)  -0.019625dprime  e2
(6c)
dnetexport  -30.11515 * d(unemp)  13.39481 * d2  e3
Substituting (6b) into (6c) we get:
11
(6c) '
dnetexport  -30.11515 * [-0.019625dprime  e2]  13.39481 * d2  e3 
 0.59101 * dprime  13.39481 * d2 - 30.11515 * e2  e3
Substituting (6a), (6b) and (6c)' into (5) we get:
(5) ''
Min
(0.124585 * dgovexp - 0.480559 * d3  e1  D(dcpi) * ) 2 
(-0.019625dprime  e2  D(unemp) * ) 2  (0.59101* dprime  13.39481* d2 - 30.11515 * e2  e3  D(netexpor ts) * ) 2
Differentiating (5 ) '' in respect to dgovexp , and dprime we get:
(a ' )
(b ' )

 2 * 0.124585(0.124585 * dgovexp - 0.480559 * d3  e 1  D(dcpi) * )  0
dgovexp

 2 * -0.019625(-0.019625dprime  e2  D(unemp) * ) 
dprime
 2 * 0.59101(0.59101* dprime  13.39481* d2 - 30.11515 * e2  e3  D(netexpor ts) * )  0
Solving (a') and (b') we get:
( a '' )
dgovexp  3.857278d3 - 8.02665 * e1  8.026648 * D(dcpi) *
(b '' )
dprime  35.63596 * e2  0.03925 * D(unemp) * -15.8329 * d 2  1.18202 * e3  1.18202 * D(net exp orts) *
Given d3, e1, D(dcpi)*, D(unemp)*, d2, e3 and D(netexports)*, we get an optimal level
of Dgovexp and dprime – which are determined exogenously by a planner (these
optimal policy levels would minimize social damage presented in equation (5)).
We should notice that the level of policy measures taken are defined as function of
constants (parameters and targeted values for the objectives), and of the error terms of
the objectives. The authority observes the estimation errors (e1, e2, e3) and then set
policy instruments levels. Such a policy takes in consideration the fact that
econometric models are not accurate. By using estimated errors the policy maker is
improving his ability to reach closer to the targets and to minimize social loss.
12
Simulation
Let us assume that the planner determines the following targeted levels:
D(dcpi)*=-0.5%, D(unemp)*=-0.5% and D(netexports)*=+2%.
Using (6a), (6b) and (6c) I calculated the errors e1, e2 and e3.
Using (a'') and (b''), I calculated the optimal levels of dgovexp and dprime for the
period 1990.1 – 2008.3.
Figure 1 present actual and optimal levels of the rate of change in government
expenditure.
13
Figure 1
actual and optimal rate of change in governemnt
expenditure
actual
optimal
20
15
10
5
0
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
-5
-10
-15
As we can see, actual change in government expenditure is much less volatile in
comparison to the optimal desired change in government expenditure.
14
Figure 2 presents actual and optimal levels of the rate of change in the prime interest
rate.
Figure 2
actual and optimal rate of change in prime rate
20
15
actual
optimal
10
5
0
19
90
19 .2
91
19 .2
92
19 .2
93
19 .2
94
19 .2
95
19 .2
96
19 .2
97
19 .2
98
19 .2
99
20 .2
00
20 .2
01
20 .2
02
20 .2
03
20 .2
04
20 .2
05
20 .2
06
20 .2
07
20 .2
08
.2
-5
-10
-15
-20
-25
As we can see, the actual rate of change in the prime rate is moving in the same
direction as the optimal change of the prime rate.
15
Optimal forecasted levels of targeted economic variables versus actual levels
Given that government authorities would have used the model, presented in this
paper, to activated the optimal rate of change in government expenditures and prime
rate during the period 1990.1 – 2008.3, I forecasted the rate of change in inflation
rate, unemployment rate and trade balance deficit.
Figures 3, 4, and 5 present actual versus optimal levels.
16
19
90
19 .2
91
19 .3
92
19 .4
94
19 .1
95
19 .2
96
19 .3
97
19 .4
99
20 .1
00
20 .2
01
20 .3
02
20 .4
04
20 .1
05
20 .2
06
20 .3
07
.4
19
90
19 .2
91
19 .2
92
19 .2
93
19 .2
94
19 .2
95
19 .2
96
19 .2
97
19 .2
98
19 .2
99
20 .2
00
20 .2
01
20 .2
02
20 .2
03
20 .2
04
20 .2
05
20 .2
06
20 .2
07
20 .2
08
.2
19
90
19 .3
91
19 .3
92
19 .3
93
19 .3
94
19 .3
95
19 .3
96
19 .3
97
19 .3
98
19 .3
99
20 .3
00
20 .3
01
20 .3
02
20 .3
03
20 .3
04
20 .3
05
20 .3
06
20 .3
07
20 .3
08
.3
Figure 3
actual versus forecasted optimal levels of inflation rate of change
Dcpi
dcpif
3
2
1
0
-1
-2
Figure 4
dunemp
actual versus forecasted optimal levels of
unemployment rate of change
15
dunempf
10
5
0
-5
-10
Figure 5
actual versus forecasted optimal levels of
trade balance rate of change
dnetexport
dnetexportf
150
100
50
0
-50
-100
17
As we can see, the optimal forecasted level of inflation is lower than the actual level
and the rate of change in unemployment and trade of balance is much more stable
than the actual rate of change.
Optimal versus actual social loss
For each time period, we can calculate social loss as defined by (5') as well as the
potential social loss given that government authorities would have activated the
optimal rate of change in government expenditures and prime rate during the period
1990.1 – 2008.3.
Figure 6 presents actual versus "optimal" social loss, while figure 7 presents the
difference between actual and optimal social loss, excluding second quarter of 1992,
where the actual deviates sharply from optimal policy (see also table in appendix 2).
18
19
90
19 .3
91
19 .4
93
.
19 1
94
19 .2
95
19 .3
96
19 .4
98
19 .1
99
20 .2
00
.
20 3
01
20 .4
03
20 .1
04
20 .2
05
20 .3
06
20 .4
08
.1
19
90
19 .3
92
19 .1
93
19 .3
95
19 .1
96
19 .3
98
19 .1
99
20 .3
01
20 .1
02
20 .3
04
20 .1
05
20 .3
07
20 .1
08
.3
Figure 6
Log of Actual Versus Optimal Social Loss
10000
1000
100
actual
optimal
10
1
0.1
0.01
0.001
0.0001
Figure 7
The Difference Between Actual and Optimal
Social Loss
2500
2000
1500
1000
500
0
-500
19
IV. Summary
This paper presents a theoretical frame that enables us to analyze the quality of
government economic policy, and demonstrates its application by using U.S. quarterly
data for the period 1990.1-2008.3. The government is trying to minimize a social loss
function, where the loss is defined as a square of the deviation of actual from optimal
levels of targeted economic variables. The minimization is done subject to constraints
that determine the level of the targeted economic variables as a function of
government economic measures taken by the government.
In this paper, constraints are estimated as a simultaneous system of equations that
connect between the targeted (endogenous) variables and the policy measures
(exogenous variables). Minimization of the social loss subject to the system of
constraints would determine each policy measure as a function of optimal levels of
targeted variables, of estimated parameters and of the estimated error terms of the
simultaneous system. Given the calculated optimal level of policy measures, the level
of targeted economic variables and the optimal potential loss are defined.
In the relevant literature, instead of empirically estimating the structural equations, the
policy rules are obtained by a set of equilibrium constraints which comes from theory.
Instead, empirically estimating the structural equations for the economy would enable
us to use more accurate information including the use of estimated errors in order to
improve policy.
Using U.S. data, I estimated a system of simultaneous equations. The endogenous
variables are the change in inflation rate, the change in unemployment rate and the
change in trade balance deficit, while exogenous variables were economic policy
measures controlled by the government. After removing non-significant variables, the
20
system of constraints was defined. Only the change in prime interest rate and the
change in government expenses were found to be significant, while all other
exogenous variables were not significant.
Given the estimates’ simultaneous system of constraints, I present a simulation with a
planner that tries to determine optimal levels of prime interest rate and government
expenses. Assuming defined optimal levels of inflation, unemployment and trade
balance deficit, the planner minimizes the loss function subject to constraints and
determines the optimal change in the prime rate and in government expenses. Given
government optimal policy, the change in the inflation rate, unemployment rate and
trade balance deficit is determined, as well as the social loss.
I compared the actual social loss in each quarter, calculated by using the actual
change in inflation rate, unemployment rate and trade balance deficit, to optimal
social loss calculated for optimal levels of government policy (according to the
suggested model). We should notice that during the nineties, the actual social loss is
much larger than the optimal social loss, while during the 2000's the gap is much
smaller. We can also see that the actual change in government expenditure is much
less volatile in comparison to the optimal desired change in government expenditure
while the actual rate of change in the prime rate is moving in the same direction as the
optimal rate of prime rate.
I should emphasize that optimum levels of endogenous variables in the simulation are
for demonstration purposes and not necessarily equal to real government optimum
levels.
21
Appendix 1
System: SYS03
Estimation Method: Two-Stage Least Squares
Sample: 1990:3 2008:2
Included observations: 72
Total system (balanced) observations 216
Prob. t-Statistic Std. Error Coefficient
0.0053 2.815335
0.0003 -3.654187
0.0000 -7.155182
0.0763 -1.781049
0.0069 2.728402
0.044252 0.124585
0.131509 -0.480559
0.002743 -0.019625
16.90865 -30.11515
4.909397 13.39481
C(1)
C(2)
C(3)
C(4)
C(5)
2.736980 Determinant residual
covariance
Equation: D(DCPI)=C(1)*DGOVEXP+C(2)*D3
Instruments: D(DM2) DPRIME DGOVEXP DGOVRECEIPT
DNETGOVSAVE D1 D2 D3 C
Observations: 72
0.016389 Mean dependent var
0.186141 R-squared
0.576056 S.D. dependent var
0.174514 Adjusted Rsquared
19.17510 Sum squared resid
0.523383 S.E. of regression
2.396311 Durbin-Watson
stat
Equation: D(UNEMP)=C(3)*DPRIME
Instruments: D(DM2) DPRIME DGOVEXP DGOVRECEIPT
DNETGOVSAVE D1 D2 D3 C
Observations: 72
0.000000 Mean dependent var
0.418969 R-squared
0.212445 S.D. dependent var
0.418969 Adjusted Rsquared
1.861881 Sum squared resid
0.161937 S.E. of regression
1.350228 Durbin-Watson
stat
Equation: DNETEXPORT=C(4)*D(UNEMP)+C(5)*D2
Instruments: D(DM2) DPRIME DGOVEXP DGOVRECEIPT
DNETGOVSAVE D1 D2 D3 C
Observations: 72
5.064996 Mean dependent var
0.041472 R-squared
21.09676 S.D. dependent var
0.027778 Adjusted Rsquared
30289.68 Sum squared resid
20.80167 S.E. of regression
2.008938 Durbin-Watson
stat
22
Appendix 2
actualoptimal
272.7139
35.00415
86.64828
6.981691
68.93788
41.00378
77.8414
122.8721
36.59608
138.796
20.9222
87.90471
23.06004
20.22669
-4.33913
25.2837
73.36688
126.1553
14.18991
39.24251
-4.5306
5.066887
32.72137
41.81961
19.4784
-0.36864
0.542032
161.082
20.27459
4.492652
43.25133
1.792252
-37.8394
7.898017
143.7977
optimal
2.321866
7.027815
1.374278
0.140818
12.64356
39.00222
19.26841
75.80888
13.9393
0.247766
0.106574
5.708692
4.842885
0.757846
6.109527
0.316046
0.388641
0.115518
18.49341
23.27112
17.41522
13.35796
12.35773
12.53663
7.451201
7.790248
4.173479
2.337129
2.732929
0.384922
1.972657
10.97517
45.0516
65.81326
1.318943
actual
275.0357
42.03197
88.02255
7.122509
81.58144
80.006
97.10981
198.681
50.53538
139.0437
21.02877
93.6134
27.90292
20.98454
1.770397
25.59974
73.75552
126.2708
32.68332
62.51363
12.88462
18.42484
45.0791
54.35624
26.9296
7.421608
4.715511
163.4191
23.00752
4.877574
45.22399
12.76742
7.21221
73.71128
145.1166
2000.1
2000.2
2000.3
2000.4
2001.1
2001.2
2001.3
2001.4
2002.1
2002.2
2002.3
2002.4
2003.1
2003.2
2003.3
2003.4
2004.1
2004.2
2004.3
2004.4
2005.1
2005.2
2005.3
2005.4
2006.1
2006.2
2006.3
2006.4
2007.1
2007.2
2007.3
2007.4
2008.1
2008.2
2008.3
actualoptimal
163.6351
60.70892
2303.134
1725.848
42.50045
32.02403
1106.633
18863.1
297.6822
233.9737
108.1156
924.3821
90.42925
25.36571
24.86998
475.3622
26.77915
33.03586
-3.14159
140.5861
997.838
105.7282
387.9561
231.5728
429.8938
646.4907
336.4326
222.6127
170.292
264.8409
145.4209
684.8842
61.83876
-2.98961
378.1906
462.5066
169.4422
31.45208
23
optimal
1.158359
0.174145
10.65569
6.450327
1.97958
13.15576
41.32788
0.002133
8.944282
0.084322
0.020403
0.018108
0.006864
0.037962
0.013405
35.21598
13.21965
11.69613
12.61992
0.743799
1.138836
0.059932
3.385642
0.253782
0.000685
0.00038
0.028696
1.636604
0.208046
0.005877
0.00793
0.001061
0.030759
7.972284
0.877543
0.164063
3.412016
1.926792
actual
164.7935
60.88306
2313.79
1732.298
44.48003
45.17979
1147.96
18863.11
306.6265
234.058
108.136
924.4002
90.43612
25.40367
24.88338
510.5782
39.9988
44.73198
9.478337
141.3298
998.9768
105.7882
391.3417
231.8266
429.8945
646.4911
336.4613
224.2493
170.5001
264.8468
145.4288
684.8853
61.86952
4.982672
379.0681
462.6707
172.8543
33.37888
1990.3
1990.4
1991.1
1991.2
1991.3
1991.4
1992.1
1992.2
1992.3
1992.4
1993.1
1993.2
1993.3
1993.4
1994.1
1994.2
1994.3
1994.4
1995.1
1995.2
1995.3
1995.4
1996.1
1996.2
1996.3
1996.4
1997.1
1997.2
1997.3
1997.4
1998.1
1998.2
1998.3
1998.4
1999.1
1999.2
1999.3
1999.4
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