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The Productivity of Government Spending in Asia: 1983-2000

Jonathan E. Leightner, Ph.D. Phone: (706) 667 - 4545 Augusta State University Fax: (706) 667 - 4064 2500 Walton Way e-mail: jleightn@aug.edu Augusta, Georgia 30904-2200 USA

Submitted to Dr. Tsu-tan Fu for possible presentation at

The Third Asian Conference on Efficiency and Productivity Growth

Abstract: By building upon Branson and Lovell (2000), Leightner (2002) develops a new analytical technique, named “Reiterative Truncated Projected Least Squares” (RTPLS), which produces reduced form estimations while greatly reducing the influence of omitted variables. Unfavorable omitted variables make observations appear to be less efficient than other observations. The first stage of RTPLS uses an output oriented variable returns to scale Data Envelopment Analysis to project data to the best practice frontier, which eliminates the influence of unfavorable omitted variables. After each stage of RTPLS is finished, the best practice observations for that stage are eliminated and another stage is conducted. This reiterative process makes it possible to trace out the true relationship between the dependant and independent variable under progressively less favorable omitted variables. Leightner (2002) documents the first 30 simulation tests of RTPLS and finds that OLS produces at least 2 times more error than RTPLS when omitted variables interact with the included independent variable. RTPLS contains the additional advantage of not requiring the construction of complex systems of equations to find reduced form estimates. Leightner (2002) uses RTPLS to estimate government spending and money supply multipliers for Thailand for 1993-2000. In this paper, I apply RTPLS to annual panel data on government spending and GDP from 1983 to 2000 for the following 24 Asian and Pacific countries: Azerbaijan, Bangladesh, Bhutan, Cambodia, China, Fiji, Hong Kong, India, Indonesia, Kazakhstan, S. Korea, Kyrgyz, Malaysia, Nepal, New Guinea, Pakistan, Philippines, Singapore, Sri Lanka, Taiwan, Thailand, Uzbekistan, Vanuatu, and Viet Nam. RTPLS will produce estimates for the government spending multiplier for these countries and will show how omitted variables have affected these multipliers across countries and over time. Branson, Johannah and C.A. Knox Lovell, “Taxation and Economic Growth in New Zealand,” in G.W. Scully and P.J. Caragata (eds.) Taxation and the Limits of Government (Boston: Kluwer Academic Publishers, 2000), 37-88. Leightner, Jonathan E. The Changing Effectiveness of Key Policy Tools in Thailand, Final Report submitted to East Asian Development Network, March 1, 2002.

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The Productivity of Government Spending in Asia: 1983-2000

The purpose of this study is to measure the productivity of government spending

in Asia between 1983 and 2000 and to show how that productivity has changed over

time, especially in the wake of Asia’s financial crisis. The productivity of government

spending will be measured as the change in Gross Domestic Product (GDP), as

measured in billions of US dollars, that results from a one billion US dollar increase in

government purchases of final goods and services.

In order to correctly estimate government spending multipliers, the influence of

numerous variables that interact with government policy must be incorporated into the

estimation procedure. Incorporating these variables into the model is particularly difficult

for Asia because these variables include some immeasurable forces, like (1) rising

international expectations during the “Asian Miracle”, then plummeting international

expectations during the “Asian Crisis,” (2) community effects, where what is happening

in one Asian country affects what is happening in other Asian countries, and (3)

differences in what governments purchase across countries and time.

Building on Branson and Lovell (2000), Leightner (2002) created a new analytical

technique named Reiterative Truncated Projected Least Squares (RTPLS) that

produces reduced form estimations while greatly reducing the influence of omitted,

unknown, and immeasurable variables. This new technique makes it possible to

estimate government policy multipliers that reflect the influence of the numerous

variables that interact with government policy without having to measure these variables

and without having to even know what these variables are.

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The first stage of RTPLS is Two Stage Least Squares (2SLS), where the first

stage is replaced by an output oriented frontier analysis (or data envelopment analysis –

DEA). By projecting all data to this frontier, the influence of unfavorable omitted

variables is eliminated. The second stage regression then estimates the relationship

between the dependant variable and the included variable when the omitted variables

are at their most favorable level. Before the next RTPLS iteration is conducted, the

observations that determined the frontier in the previous iteration are eliminated.

Additional iterations are conducted until the sample size is too small to support an

additional iteration. Each iteration produces a slope estimate of the relationship

between the dependant and included variable under progressively less favorable levels

of omitted variables. A given iteration’s slope estimate is entered into the data for the

observations that determined the frontier in that iteration. A final regression is then

conducted between these slope estimates and a constant, the inverse of the included

independent variable, and the ratio of the dependant variable to the included

independent variable. The data is then plugged back into the equation estimated in this

final regression in order to determine a slope estimate for each observation. These

slope estimates are reduced form estimates that capture the influence on the dependent

variable of everything that is correlated with the included independent variable.

The results of the first 30 simulation tests of RTPLS indicate that OLS produces

an average of 125 percent more error than RTPLS when omitted variables cause the

true coefficient for the included variable to vary by ten percent. When the omitted

variables cause the true coefficient to vary by a hundred and a thousand percent, then

OLS produces an average of 112 percent and 401 percent (respectively) more error

than RTPLS. RTPLS produces reduced form coefficients that capture all the forces

correlated with the included independent variable without having to construct

complicated systems of hundreds or thousands of equations.

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The remainder of this paper is organized as follows. Section 2 explains the

analytical techniques used to eliminate the influence of omitted variables and to

calculate the productivity of government purchases. Section 3 presents the Asian data.

Section 4 presents the results. Section 5 concludes.

III Analytical Techniques:

The analytical technique used in this paper is built upon a technique introduced

by Branson and Lovell (2000). The Branson--Lovell method is similar to an instrumental

variables method, like two stage least squares (2SLS), which is used to correct for

simultaneous equation bias. In the 2SLS method, all endogenous variables are

regressed on all exogenous variables. Instruments for the endogenous variables are

then constructed by projecting the endogenous variables to the resulting regression line.

The instruments are then used to estimate the desired equation. In essence, 2SLS

throws away all the variation in the endogenous variables that cannot be explained by

the exogenous variables.

The Branson--Lovell method replaces the first stage in 2SLS with a linear

programming data envelopment analysis (DEA), which constructs a best practice

frontier. DEA techniques are based upon Shephard (1970), Debreu (1951), Farrell

(1957), Charnes, Cooper, and Rhodes (1978), and Banker, Charnes, and Cooper

(1984). This best practice frontier shows the relationships between the dependent

variable and the included independent variables when the omitted variables are at their

most favorable levels. All observations are then projected to this frontier, thus purging

from the data the variation caused by the omitted variables. The projected data points

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are then used to estimate the desired equation. For purposes of clarification, the

Branson--Lovell method will be called “Projected Least Squares” (PLS) in this study.

Whereas OLS places a line through the middle of the data, DEA draws a facetted

envelope around the top of the data by drawing a line between the best-practice

observations. Best-practice is defined as those observations that produce the most

output (dependent variable) for a given level of inputs (independent variables) or uses

the least inputs for a given level of output. In most previous applications of DEA, the

distance an observation falls below (or to the right of) this frontier is a measure of

inefficiency. OLS assumes that all the variation from the OLS line is random error, and

DEA typically assumes that all the variation from the DEA frontier is inefficiency.

The first stage of Projected Least Squares (PLS) gives a new interpretation to the

distance between the DEA frontier and a given observation. Under PLS, an observation

falls below the best practice frontier if unfavorable omitted variables have affected that

observation.1 The ratio of maximally expanded output production to actual output

production (Φ) provides a measure of the influence of unfavorable omitted variables on

each observation.2

Denote the outputs (or dependant variable) of an observation by yim, i=1,..., I,

m=1,...,M and the inputs (or independent variables) of an observation by xin, i=1,...,I,

n=1,...,N. Consider the following DEA problem:

(1) Objective: max Φ

subject to Σi λi xni < xno , n = 1,..., N

Φymo < Σi λi ymi , m = 1,...,M

Σi λi = 1; λi >0, i=1,...,I .

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This problem is solved I times, once for each observation in the sample. For

observation "o" under evaluation, the problem seeks the maximum radial expansion in

all outputs ymo consistent with best practice observed in the sample, i.e., subject to the

constraints in the problem.

The first stage of PLS calculates this best practice frontier between the output

(dependent variable) and inputs (independent variables) and then projects each

observation to the frontier by multiplying actual output by Φ, the measure of the

influence of unfavorable omitted variables. By projecting the data to the frontier, the

influence of unfavorable omitted variables is eliminated.

In order to test PLS, three series of one hundred random numbers each were

computer generated. The values of these random numbers range between zero and

one thousand. The three data series are shown in the first three columns of Table 1

and are labeled X1, X2, and X3. The fourth column of Table 1 shows Y1, which was

constructed via the equation Y1 = 50 + X1 + 2 X2. The first six columns of Table 1 were

generated and then the rows of this table were sorted by the increasing numerical value

of column 1.

Figure 1 plots the relationship between Y1 and X1. Each point on Figure 1 is

identified by the corresponding value for X2. Notice that the lower, right-hand envelope

of the points in Figure 1 corresponds to the smallest values of X2. Notice also that the

upper, left-hand envelope of the points in Figure 1 correspond to the largest values of

X2. Figure 1 shows that, as one moves from the lower to the higher parts of this figure,

the true relationship between Y1 and X1 is being shifted up by increasing values of X2.

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When the analytical techniques described above are applied to this data, they

construct a best practice frontier consisting of the left handed and upper envelopes of

this data. Column 5 of Table 1 shows the omitted variables scores (Φ), which will be

multiplied by Y1 in order to project the data to the frontier. Figure 2 shows the data after

the dependent variable has been projected to the frontier. The upper portion of this

frontier shows the relationship between X1 and Y1, when X2 is held relatively constant at

its highest values. The second stage of PLS then uses the projected data points in a

regression to estimate the true relationship between X1 and Y1.

The upper part of Figure 2's frontier is extremely close to the true relationship

between X1 and Y1 (when X2 is at its highest level). In contrast, the three points that

make up the left hand section of this frontier have nothing to do with the true

relationship between X1 and Y1 (when X2 is at its highest level). From where did these

three points come? The data in Figure 1 actually correspond to 100 lines showing the

true relationship between X1 and Y1, one for each separate value of X2. If these lines

are like one hundred parallel grain lines in a piece of wood, then the three points in the

lower left side of Figure 2 are the smallest values for the end-grain of that wood. For

PLS to work as well as possible, these three points must be eliminated before the

second stage regression is conducted. “Projected Least Squares” (PLS) does not

eliminate end-grain observations but “Truncated Projected Least Squares” (TPLS) does

eliminate end-grain observations.

It is possible to have end-grain observations at both ends of the frontier. By

looking at Figure 2, a researcher can tell that it is extremely likely that the three points

which correspond to the smallest values of Y1 are from end-grain observations. Column

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6 of Table 1 shows the Y1 values after they are projected to the frontier. In order to

better show the end-grain observations, the rows of Table 1 were sorted by increasing

numerical value of the included independent variable (X1). Lower-left end-grain

observations are observations that correspond to relatively small projected Ys – thus

the first three observations in Table 1 are endgrain. Upper-right end-grain observations

show up as the horizontal section that begins immediately after the last efficient

observation; for example, the last six observations in Table 1. Before running the

second stage regression in TPLS, the first three and the last six observations in Table 1

were eliminated.

Remember that Y1 = 50 + X1 + 2 X2. Thus the true value for dY1/dX1 is one.

When X2 is omitted, then OLS produces an estimate of 0.883 for dY1/dX1, PLS

produces an estimate of 1.103, and TPLS produces an estimate of 1.020. Furthermore

adding some random error to Y1 does not noticeably change these results. The X3

values listed in Table 1 were used to construct this error term. The average value for X3,

492.33, was subtracted from each individual value of X3 and the result was multiplied by

0.1 in order to create ε. Y2 was created by adding ε to each Y1.3 When random error is

included and X2 is omitted, OLS produces an estimate of 0.890 for dY2/dX1, PLS

produces an estimate of 1.103, and TPLS produces an estimate of 1.024.

However, variations in the values of the efficient observations can noticeably

affect the results of TPLS. For example, if the following two additional efficient

observations, X1 = 0, X2 =1000 and X1 = 1000, X2 =1000, were added to Table 1, then

TPLS would produce a coefficient that would exactly equal the true coefficient. In Figure

I, these additions would produce two new points at Y1 = 2050, X1 = 0 and Y1 = 3050, X1

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=1000 which would result in a new frontier that has a slope of one (ΔY1 = 1000, ΔX1

=1000), the true value for dY1/dX1. However, if instead, the following two observations

were added, then the slope would be 0.80: X1 = 0, X2 =1100, and X1 = 1000, X2 =1000.

Likewise, if X1 = 0, X2 =1000, and X1 = 1000, X2 =1100 were added, then the slope

would be 1.20. TPLS works perfectly if the values of the omitted variables are the same

for each of the efficient points that determine the frontier. The relatively largest values

for the omitted variables will correspond to the efficient points that determine the frontier,

but only rarely would the value of these omitted variables perfectly match each other. If

after using TPLS, the efficient observations are deleted, then another iteration of TPLS

could be conducted. Additional iterations can be conducted until the sample size

becomes too small. Conducting multiple iterations of TPLS improves the results by

averaging out the effects of variations in the values of the omitted variables that

correspond to the efficient observations – the observations that determine the frontier.

Conducting multiple iterations of TPLS is even more important if omitted

variables interact with the included variable. For example, if Y3 = 50 + 100X1 + 10X2 +

0.1X1X2, then dY3/dX1 is 100 + 0.1X2. If Y3 is estimated without the interaction term

(X1X2), then OLS and TPLS produce estimates for dY3/dX1 of approximately4 100 +

0.1*(531.14), because the average value for X2 is 531.14. However, if both the

interactive term and X2 are omitted, then OLS and TPLS produce very different results.

Specifically, OLS continues to plug the average value for X2 into 100 + 0.1X2, whereas

TPLS plugs the mean X2 for only the efficient observations into 100 + 0.1X2. Thus the

OLS estimate for dY3/dX1, when both X2 and X1X2 are omitted, is 149.76; in contrast the

TPLS estimate is 193.45. When both X2 and X1X2, are omitted, then each iteration of

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TPLS produces progressively smaller estimates for dY3/dX1 because the efficient

observations that determine each successive frontier will correspond to progressively

smaller values for the omitted variable, X2. This makes it possible for Reiterative

Truncated Projected Least Squares (RTPLS) to trace out the effects of omitted

variables that interact with the included variable.

Procedurally, RTPLS starts with a series of TPLSs. After the first TPLS is

complete, the efficient observations are deleted, than TPLS is re-run. The first TPLS run

traces out the relationship between the dependent variable and the included

explanatory variables when the excluded explanatory variables are at their most

favorable level. The second TPLS traces out the effects when the excluded variables

are at their second most favorable level. Likewise the nth TPLS run traces out the

effects when the excluded variables are at their nth most favorable level. Each

successive TPLS run is conducted on a slightly smaller sample than the previous run.

Additional TPLS runs are conducted until the sample size becomes too small to support

an additional run. The TPLS estimated coefficient for a given iteration is entered into

the data set for the efficient observations eliminated by that iteration, which were not

end-grain observations. 5 The TPLS coefficient is then treated as the dependent

variable and regressed on a constant, the inverse of the included independent variable

and the ratio of the original dependent variable to the included independent variable.

The following derivation shows why these regressors are used.

(2) Y = α0 + α1 X1 + α2 X2 + α3 X1X2.

(3) dY/dX1 = α1 + α3 X2 (Derivative of equation 2).

(4) Y/X1 = α0/X1 + α1 + α2 X2/X1 + α3X2 (Divide both sides of equation 2 by X1).

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(5) α1 + α3X2 = Y/X1 - α0/X1 - α2 X2/X1 (Rearranging equation 4).

(6) dY/dX1 = α1 + α3 X2 = fn(Y/X1, 1/X1) (From equations 3 and 5).

When equation 6 is estimated, a constant is used to capture the α1 part of dY/dX1, and

Y/X1 and 1/X1 are used to capture the α3X2 part of dY/dX1. In other words, Y/X1 and 1/X1

are used as a proxy for the omitted, unknown, or immeasurable X2. This makes intuitive

sense because Y is co-determined by the known X1 and the unknown X2, therefore the

combination of Y and X1 contains information about X2. Data for Y/X1 and 1/X1 are

plugged back into the estimate of equation 6 to produce RTPLS estimates of dY/dX1 for

each observation.

In order to make RTPLS non-arbitrary, several rules must be established. For all

estimations in this paper, the following rules were used.6

A. Truncation rules (applied after the data is sorted by the included independent

variable):

1. The three percent of the observations that correspond to smallest

values for the included independent variable are considered lower left

hand endgrain and are not used when the second stage regression is

run. When applying this rule, the number of observations not used is

always rounded up to the next integer.

2. All observations (up to a maximum of 33 percent of the remaining

observations) with values for the included independent variable that

are greater than the last efficient observation’s value are considered

upper right hand end grain. These observations will be in a horizontal

section of the frontier, and they are not used when the second stage

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regression is run. If more than 33 percent of the remaining

observations are in this horizontal section, then only the last ten

percent are eliminated.

B. Iteration rule: an additional iteration is not conducted if that iteration’s second

stage regression would use fewer than ten observations.

Leightner (2002) reports on the thirty simulation runs of the entire RTPLS

procedure that have been completed as of this date. Ten sets of random numbers for

X1 and X2 were computer generated, where each number was between zero and one

thousand. For simulation runs 1-10, the equation Y = 50 + 100X1 + X1X2 was used to

define the dependant variable. For simulation runs 11-20, the equation Y = 50 + 100X1

+ 0.1X1X2 was used, and for simulation runs 21-30, the equation Y = 50 + 100X1 +

0.01X1X2 was used. Thus for simulation runs 1-10, the true value for dY/dX1 could

range between 100 and 1100 (for these runs, dY/dX1 = 100 + X2 and X2 ranges from 0

to 1000). For simulation runs 11-20, dY/dX1 could range from 100 to 200, and for

simulation runs 21-30, dY/dX1 could range from 100 to 110. Thus, the omitted variable,

X2, makes a thousand percent, hundred percent, and a ten percent difference in the true

value of dY/dX1 in simulation runs 1-10, 11-20, and 21-30 respectively.

Leightner (2002) then calculated the ratios of the mean error from OLS to the

mean error from RTPLS and the maximum error from OLS to the maximum error from

RTPLS.7 He finds that, on average, OLS produces 5.01 times, 2.12 times, and 2.25

times as much error as RTPLS produces when the omitted variable makes a thousand,

hundred, and a ten percent difference respectively. On average, the observation with

the most error under OLS had 9.68 times, 2.62 times, and 1.64 times more error than

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the RTPLS observation with the most error when the omitted variable makes a

thousand, hundred, and ten percent difference.

These simulation tests indicate that RTPLS is far superior to OLS when there are

omitted variables that interact with the included variables. Furthermore, RTPLS carries

the great advantage of producing reduced form estimates without having to construct

(and solve) complicated systems of equations. Moreover, to the extent that

autocorrelation and heteroskedasticity are caused by omitted variables, RTPLS reduces

these problems.

III. The Data

All the data was down loaded from http://www.adb.org/documents/Books/Key

_Indicators/2000/default.asp?p=ecnm. The data is presented in Table 2: Panel A gives

GDP and Panel B gives government purchases of final goods and services. All data is

given in billions of US dollars. The four Asian countries hardest hit by the crisis were

Thailand, South Korea, Indonesia, and Malaysia. The first three of these countries

agreed to IMF conditions in order to receive large IMF loans and remained relatively

open to foreign capital flows. Malaysia did not agree to IMF conditions, did not receive

an IMF loan, and imposed relatively strong controls on foreign capital flows.

Figure 3 shows what happened to GDP from 1983 to 2000 for these four crisis

countries. The 1997-1998 fall in GDP, due to the crisis, appears to be directly related to

the 1985-1996 growth in GDP. South Korea, with the greatest growth between 1985

and 1996, experienced the greatest fall from 1997 to 1998 and Malaysia, with the

smallest growth, experienced the smallest fall. Figure 4 shows what happened to GDP

in four relatively large8 developing Asian countries. GDP did not fall in Mainland China

and India with the Asian crisis, but it did fall in Taiwan and Hong Kong. Figure 5 shows

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what happened to GDP in four relatively small developing Asian countries. Singapore

and the Philippines experienced a noticeable fall in GDP in 1997; whereas, Pakistan,

Bangladesh, and Sri Lanka did not. Table 2 indicates that only 8 out of 24 Asian and

Pacific countries did not suffer a 1% or greater annual fall in GDP between 1997 and

1999 (Azerbaijan, Bangladesh, Bhutan, China, India, Pakistan, Sri Lanka, and

Uzbekistan). It is important to realize that all (or a major part of) the fall in GDP (as

measured in US dollars) could be due to devaluations and depreciations of the national

currencies of these Asian countries.

IV. The dGDP/dG Results

The empirical results 9 from using RTPLS to estimate government spending

multipliers for developing Asian countries are presented in Table 3. On average,

dGDP/dG was 7.92 in 1983, slowly grew to 8.18 in 1997, fell to 8.14 by 1999, but more

than rebounded to 8.26 in 2000. The mean value of 7.92 for dGDP/dG in 1983 means

that, on average, an increase in government spending of 1 billion US dollars in 1983

would have caused GDP to rise by 7.92 billion US dollars.

Why Government spending causes GDP to rise by much more than the direct

government spending is best explained with an example. What the government pays to

build roads becomes income for the road builders. If the road builders buy food with

part of their income, then what they pay for the food becomes income for the farmers

who may buy tractors with part of that income. The roads, the food, and the tractors are

all final goods and services and all of them would be included in GDP, if they are not

imported. In a simple undergraduate macroeconomic model (where only consumption

and investment are related to income) the value for the government spending multiplier

is 1/[1-(MPC+MPI)] where MPC is the marginal propensity to consume and MPI is the

marginal propensity to invest. If MPC+MPI is 0.875 then the simple undergraduate

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model produces a multiplier of 8. More complex macroeconomic models would include

the effects of income on imports, on interest rates (which would further effect

consumption and investment), on the exchange rate (which would further effect imports

and exports), and on etc. It is important to realize that RTPLS produces reduced form

estimates for dGDP/dG that capture all the ways that GDP and government purchases

are correlated without having to construct complicated macroeconomic models.

Furthermore, RTPLS traces out how dGDP/dG changes due to forces that interact with

government spending.

Figures 6, 7, and 8 graphically depict dGDP/dG over time for select countries.

Figure 6 shows dGDP/dG for the crisis countries. dGDP/dG fell for South Korea and

Thailand between 1997 and 1998 and for Indonesia and Malaysia between 1998 and

1999. Furthermore, Thailand’s and Indonesia’s dGDP/dG appear to track each other’s

dGDP/dG for 1984 to 1993 and Malaysia’s and Indonesia’s dGDP/dG appear to track

each other’s dGDP/dG between 1993 and 1999. This apparent tracking effect is

probably due to similar forces interacting with government spending in these countries.

In Figure 7, Hong Kong’s dGDP/dG and the Philippine’s dGDP/dG appear to

track each other for 1988 to 2000. Mainland China’s and Taiwan’s dGDP/dGs appear

to track each other for 1983 to 1998. In Figure 8, dGDP/dG usually stays in a relatively

narrow ban between 7.9 and 8.4 for India, Pakistan, Nepal, and Sri Lanka. Bhutan’s

dGDP/dG is the second to the lowest (the islands of Vanuatu are always the lowest) of

all the countries analyzed.

Bangladesh has the highest dGDP/dG of all the countries analyzed between1990

to 2000. Prior to 1990, Bangladesh’s dGDP/dG was very similar to that of India and

most of India’s other neighbors. Although dGDP/dG changes over time for most of the

countries analyzed, these changes appear to be relatively smooth in comparison to

Bangladesh’s change in dGDP/dG between 1989 and 1990 (see Figure 8).10

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The dGDP/dG results found for Thailand in this study, which used annual panel

data from 24 developing Asian and Pacific countries between 1983 and 2000, appear to

conflict with the dGDP/dG results found using monthly data for just Thailand between

January 1993 and December 2000, as reported in Leightner (2002). Leightner (2002)

found a January 1993 to June 1997 average monthly dGDP/dG of 2.95 and a July 1997

to December 2000 average monthly dGDP/dG of 0.76. In this present study Thailand’s

average annual dGDP/dG was 8.29 for 1993-1996 and 8.15 for 1998-2000. There are

several possible explanations for this apparent discrepancy.

First, the difference in the Thai results found in this study versus those found in

Leightner (2002) could be due to the base currency used. In this study, GDP and

government purchases were translated into US dollars; whereas, Leightner (2002) used

the Thai data as expressed in Thai baht, without converting it to US dollars. To test the

effects of using data in baht versus dollars, the monthy data used in Leightner (2002)

was translated into US dollars and the analysis that Leightner (2002) conducted was re-

done. When this was done, the average dGDP/dG for January 1993 to June 1997 was

2.85 [Leightner (2002) found 2.95] and for July 1997 to December 2000 it was 0.70

[Leightner (2002) found 0.76]. Therefore, using dollars instead of Thai baht cannot

explain the differences between this current study and Leightner (2002).

The apparent discrepancy between this paper’s results and Leightner (2002)

could be due to differences in what is included in government spending. This current

study used only government spending on final goods and services (which is what is

included when calculating GDP using the expenditures approach); in contrast, Leightner

(2002) used all government expenses (which is what is used to calculate a government

surplus or deficit). All government expenses would include transfer payments; whereas,

government spending on final goods and services would not. Leightner (2002) used all

government expenses because monthly data on government purchases of final goods

and services is not available. However, quarterly data on government purchases of

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final goods and services (for 1993, first quarter, to 2001, third quarter) is available

through the Bank of Thailand’s web page. When RTPLS is used with this quarterly

Thai data, average dGDP/dG for 1993-1996 is 8.23 (in this study it was 8.29) and

average dGDP/dG for 1998-2000 is 7.89 (in this study it was 8.15). Therefore the panel

data for 24 different countries produced average RTPLS estimates for Thailand that are

within three percent of the average RTPLS results from using quarterly time series data

on just Thailand. For the case of Thailand, RTPLS produced extremely robust results.

The differences between the results obtained in this study and Leightner (2002)

are due to differences in what was included in government spending. It makes sense

that government purchases of final goods and services (which was used in this study)

would have a much bigger multiplier effect than total government expenses (which was

used in Leightner, 2002). The RTPLS reduced form estimates of dGDP/dG produced

when G includes transfer payments would include the fact that when GDP falls then

transfer payments increase. In contrast, when G does not include transfer payments,

then RTPLS estimates of dGDP/dG would not include this negative correlation between

GDP and transfer payments.

V. Conclusion

Governments need to know how productive changes in government spending are

in producing desired changes in gross domestic product. More precise estimates of

dGDP/dG would make it possible for governments to better control their economies.

Statistical methods used in the past to estimate dGDP/dG involve constructing complex

systems of equations and these methods produce a single numerical estimate for

dGDP/dG for the entire time period studied.11 This paper uses a new statistical method,

named reiterative truncated projected least squares (RTPLS), to estimate dGDP/dG for

24 Asian and Pacific developing countries between 1983 and 2000. RTPLS produces

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reduced form estimates without having to construct complex systems of equations and

these estimates show how forces that are not explicitly modeled affect the estimate.

Whereas traditional regression technique would produce one value for dGDP/dG for all

24 countries studied for all the years studied, RTPLS produces a separate multiplier for

each country and year in the data. This makes it possible to see how the multiplier is

changing over time and, thus, to design more appropriate responses to any given set of

circumstances. For example, if a single value for dGDP/dG was estimated using

traditional methods for the Philippines, that information would be no where near as

helpful to the government of the Philippines as Figure 7 which shows that dGDP/dG is

falling over time and how rapidly it is falling. Likewise RTPLS clearly shows that

Bhutan’s dGDP/dG is lower than its neighbors and rising (Figure 8). Although adding

dummy variables to traditional methods can show how dGDP/dG differs for different

countries or for different years, dummying both years and countries when using

traditional methods is impossible because the number of right hand variables would

then exceed the number of observations. There is no way for traditional statistically

methods to show the depth of information provided by Figure 8 on Bhutan. RTPLS

holds great promise. It is a powerful tool for analyzing the productivity of all things (not

just government spending) and it analyzes productivity while minimizing the influence of

un-modeled forces that interact with the included variables.

19

-100 0 100 200 300 400 500 600 700 800 900 1000 11000

100

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529

471

407

619

734

926

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447

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63

518

778

274

937

780

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687

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905832

496

217

921

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56

473

803

415562

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689

754

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765

269

856

866

311

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24

899

651

473730865

382

839

387

750

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227

610630

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793910

935

0

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730 570

140

153

731

604

907

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74

99

101

796

152

615

198

173

963

774

950

155

75

872

908

464

787

653

406

542

61

415

27

582903

193347

545

340

662

X1

Y

Figure 1: The Data for Simulations 1 & 2Y = 50 + X1 + 2*X2

Numbers correspond to X2 values

20

-100 0 100 200 300 400 500 600 700 800 900 1000 11000

100

200

300

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500

600

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X1

YFigure 2: Output Projected to the Frontier

Y = 50 + X1 + 2*X2

Frontier calculated without X2

21

1982 1984 1986 1988 1990 1992 1994 1996 1998 20000

50

100

150

200

250

300

350

400

450

500

550

Year

GD

P in

billi

ons

of U

S$

Indonesia

S. Korea

Malaysia

Thailand

Figure 3: GDP for Crisis Countries in US$

22

1982 1984 1986 1988 1990 1992 1994 1996 1998 20000

100

200

300

400

500

600

700

800

900

1000

1100

1200

Year

GD

P in

billi

ons

of U

S$

China

Hong Kong

Taiw an

India

Figure 4: GDP for Large Countries in US$

23

1982 1984 1986 1988 1990 1992 1994 1996 1998 20000

10

20

30

40

50

60

70

80

90

100

Year

GD

P in

billi

ons

of U

S$

Pakistan

Nepal

Bhutan

Bangladesh

Sri Lanka

Philippines

Singapore

Figure 5: GDP for Small Countries in US$

24

1982 1984 1986 1988 1990 1992 1994 1996 1998 20006.7

6.9

7.1

7.3

7.5

7.7

7.9

8.1

8.3

8.5

8.7

8.9

9.1

9.3

9.5

9.7

9.9

Year

dGD

P/dG

Indonesia

S. Korea

Malaysia

Thailand

Figure 6: dGDP/dG for Crisis Countries

25

1982 1984 1986 1988 1990 1992 1994 1996 1998 20006.7

6.9

7.1

7.3

7.5

7.7

7.9

8.1

8.3

8.5

8.7

8.9

9.1

9.3

9.5

9.7

9.9

Year

dGD

P/dG

China

Hong Kong

Taiw an

Philippines

Singapore

Figure 7: dGDP/dG for China and Other Countries

26

1982 1984 1986 1988 1990 1992 1994 1996 1998 20006.7

6.9

7.1

7.3

7.5

7.7

7.9

8.1

8.3

8.5

8.7

8.9

9.1

9.3

9.5

9.7

9.9

Year

dGD

P/dG

India

Pakistan

Nepal

Bhutan

Bangladesh

Sri Lanka

Figure 8: dGDP/dG for India and its Neighbors

27

Table 1: The Data for Figures 1 and 2 (Means Given in Last Row)

X1 X2 X3 Y1 Φ Φ*Y1

6 152 323 360 1 360

11 734 946 1529 1 1529 16 227 227 520 3.4917 1816 17 903 802 1873 1 1873 21 511 509 1093 1.7200 1880 34 630 424 1344 1.4156 1903 50 311 43 722 2.6735 1930 51 387 209 875 2.2080 1932 51 730 626 1561 1.2377 1932 58 316 519 740 2.6273 1944 79 731 431 1591 1.2449 1981

100 610 857 1370 1.4723 2017 104 27 543 208 9.7310 2024 106 856 689 1868 1.0854 2028 120 700 42 1570 1.3069 2052 125 796 530 1767 1.1661 2061 131 63 142 307 6.7457 2071 131 61 452 303 6.8347 2071 137 518 198 1223 1.7018 2081 165 865 315 1945 1.0951 2130 175 921 43 2067 1.0389 2147 179 832 370 1893 1.1380 2154 180 963 296 2156 1 2156 187 689 276 1615 1.3406 2165 191 406 844 1053 2.0610 2170 198 872 603 1992 1.0940 2179 218 542 396 1352 1.6311 2205 232 340 855 962 2.3112 2223 236 99 282 484 4.6045 2229 262 907 157 2126 1.0641 2262 271 447 361 1215 1.8716 2274 279 591 231 1511 1.5118 2284 290 24 906 388 5.9242 2299 303 153 487 659 3.5136 2315 306 651 993 1658 1.3989 2319 307 908 804 2173 1.0679 2321 316 910 650 2186 1.0669 2332 357 570 307 1547 1.5420 2385 397 217 814 881 2.7665 2437 407 754 217 1965 1.2470 2450 420 526 483 1522 1.6210 2467 423 999 782 2471 1 2471 428 750 585 1978 1.2511 2475 439 950 350 2389 1.0393 2483 445 615 141 1725 1.4420 2487 446 173 262 842 2.9550 2488 458 866 901 2240 1.1148 2497 475 730 575 1985 1.2644 2510 493 4 405 551 4.5793 2523 500 496 839 1542 1.6397 2528 502 937 698 2426 1.0428 2530 504 926 934 2406 1.0521 2531 512 166 315 894 2.8382 2537 532 839 435 2260 1.1293 2552

541 793 469 2177 1.1755 2559

28

X1 X2 X3 Y1 Φ Φ*Y1 546 634 398 1864 1.3748 2563 553 101 281 805 3.1900 2568 596 604 267 1854 1.4024 2600 597 140 216 927 2.8055 2601 622 274 998 1220 2.1470 2619 627 562 491 1801 1.4565 2623 652 496 16 1694 1.5595 2642 669 347 971 1413 1.8786 2654 670 0 538 720 3.6877 2655 693 905 808 2553 1.0467 2672 703 75 690 903 2.9676 2680 708 407 193 1572 1.7070 2683 716 899 435 2564 1.0489 2689 716 471 422 1708 1.5746 2689 718 6 934 780 3.4499 2691 742 582 945 1956 1.3849 2709 748 619 80 2036 1.3327 2713 751 74 53 949 2.8615 2716 751 473 287 1747 1.5544 2716 753 832 275 2467 1.1013 2717 762 464 270 1740 1.5654 2724 778 545 925 1918 1.4263 2736 782 198 51 1228 2.2302 2739 788 56 831 950 2.8875 2743 799 787 37 2423 1.1355 2751 815 382 883 1629 1.6963 2763 816 269 910 1404 1.9687 2764 825 778 235 2431 1.1397 2771 841 653 305 2197 1.2666 2783 854 765 763 2434 1.1472 2792 855 415 314 1735 1.6098 2793 857 201 340 1309 2.1349 2795 884 155 944 1244 2.2626 2815 889 529 848 1997 1.4113 2818 892 349 885 1640 1.7199 2821 900 774 47 2498 1.1316 2827 905 662 367 2279 1.2419 2830 909 193 23 1345 2.1066 2833 914 803 931 2570 1.1039 2837 926 935 533 2846 1 2846 963 651 366 2315 1.2294 2846 965 687 678 2389 1.1913 2846 976 473 107 1972 1.4432 2846 989 780 691 2599 1.0950 2846 997 415 758 1877 1.5162 2846

493.34 531.14 492.33 1605.02 1.9329 2437.73

1

Table 2: The Data

Panel A: GDP in billions of US$

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

Azerbaijan 0.44 1.57 1.19 2.42 3.18 3.96 4.45 4.59 5.27

Bangladesh 11.95 14.01 14.53 15.33 17.42 18.82 20.44 29.02 30.20 30.69 31.69 33.67 37.87 39.80 41.17 42.68 44.76 45.47

Bhutan 0.18 0.19 0.19 0.22 0.28 0.28 0.27 0.28 0.24 0.25 0.24 0.27 0.31 0.33 0.40 0.40 0.44

Cambodia 1.80 1.44 1.43 1.90 1.98 2.22 2.43 3.10 3.17 3.11 2.82 3.06 3.11

China 300.40 309.09 305.24 295.47 321.40 401.06 449.02 387.77 406.09 483.05 601.08 542.53 700.22 816.49 898.25 946.31 989.47 1079.95

Fiji 1.12 1.18 1.14 1.29 1.18 1.11 1.25 1.36 1.38 1.53 1.63 1.83 1.99 2.11 2.12 1.65 1.86 1.60

Hongkong 28.88 31.89 34.19 39.88 49.66 58.89 67.22 75.62 85.94 100.88 114.21 130.23 138.20 154.20 170.24 159.01 154.07 162.60

India 205.56 203.59 212.01 232.30 257.06 284.39 281.54 305.95 271.22 272.37 287.59 330.80 364.50 386.14 419.25 426.16 454.53

Indonesia 85.39 87.61 87.31 80.03 75.92 88.77 101.46 114.41 128.19 139.11 158.01 176.87 202.10 227.40 215.78 95.44 141.31 153.25

Kazakhstan 11.76 11.92 16.64 21.04 22.16 22.14 16.87 18.26

Korea 82.31 90.58 93.46 107.61 135.18 180.60 220.70 252.61 295.22 314.76 345.70 402.50 489.24 520.17 476.48 317.09 406.08 457.20

Kyrgyz 0.87 1.11 1.49 1.83 1.77 1.64 1.25 1.30

Malaysia 30.35 33.94 31.20 27.73 32.18 35.27 38.85 44.02 49.13 59.15 66.89 74.48 88.83 100.85 100.17 72.17 79.04 89.66

Nepal 2.33 2.39 2.55 2.63 2.93 3.30 3.28 3.52 3.23 3.50 3.53 4.03 4.22 4.39 4.84 4.56 5.01 5.39

Newguinea 2.57 2.36 2.20 2.39 2.63 2.84 2.82 2.46 2.71 3.04 3.54 3.63 2.77 2.90 2.56 1.71 1.48

Pakistan 27.91 30.03 29.79 31.05 33.06 37.69 37.65 39.62 43.08 48.52 47.96 51.71 59.76 59.65 60.06 59.58 59.82 60.26

Philippines 33.21 31.41 30.74 29.87 33.20 37.89 42.57 44.31 45.42 52.98 54.37 64.08 74.12 82.85 82.34 65.17 76.16 74.73

Singapore 17.38 18.77 17.69 17.86 20.41 25.20 29.84 36.67 42.84 49.07 57.67 69.83 83.11 90.92 94.44 82.14 83.84 92.25

Srilanka 5.07 5.79 5.81 6.15 6.41 6.88 6.89 7.94 8.94 9.62 10.34 11.72 12.92 13.90 15.09 15.79 15.66 16.30

Taiwan 52.41 59.17 62.08 75.46 101.99 123.24 149.16 160.15 179.40 212.17 224.29 244.31 267.01 279.63 290.17 267.19 287.88 310.10

Thailand 40.04 41.80 38.90 43.09 50.54 61.68 72.26 85.33 98.22 111.45 125.21 144.51 168.25 182.43 151.16 111.91 122.07 122.17

Vanuatu 0.11 0.13 0.12 0.12 0.12 0.14 0.14 0.15 0.18 0.19 0.18 0.21 0.23 0.24 0.24 0.23 0.23

Vietnam 6.47 7.64 9.87 13.18 16.29 20.74 24.66 27.52 29.58 29.00 31.36

Uzbekistan 6.62 10.17 13.95 14.73 14.98 17.07 13.48

Mean 51.51 53.55 53.84 56.03 63.42 72.10 80.36 79.96 85.06 90.70 94.08 96.95 114.59 126.34 129.08 114.37 124.81 137.19

2

Panel B: Government Purchases of Final Goods and Services in billions of US$

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

Azerbaijan 0.079 0.473 0.281 0.309 0.382 0.253 0.335 0.859 0.695

bangladesh 1.487 1.735 1.775 1.921 1.981 2.206 2.804 1.218 1.249 1.366 1.569 1.644 1.753 1.751 1.798 2.019 2.054 2.079

Bhutan 0.044 0.045 0.045 0.046 0.049 0.046 0.054 0.045 0.045 0.047 0.041 0.051 0.074 0.071 0.101 0.079 0.091

cambodia 0.097 0.111 0.104 0.339 0.201 0.114 0.194 0.169 0.202 0.188 0.158 0.189 0.207

China 42.415 43.966 40.317 39.591 40.031 46.399 53.996 53.353 53.162 63.323 78.098 69.454 80.118 94.441 105.250 114.567 124.253 141.342

Fiji 0.228 0.226 0.219 0.223 0.205 0.184 0.205 0.234 0.242 0.276 0.303 0.301 0.317 0.338 0.352 0.289 0.299 0.287

hongkong 2.252 2.310 2.540 2.933 3.298 3.844 4.648 5.556 6.623 8.277 9.388 10.825 12.182 13.496 14.692 15.204 15.658 15.638

India 20.933 21.429 23.583 27.460 31.507 34.009 33.403 35.295 30.543 30.326 31.561 34.159 39.695 41.094 47.418 51.327 58.418

indonesia 8.886 8.891 9.805 8.830 7.156 7.566 8.869 10.119 10.659 12.183 14.258 14.352 15.822 17.207 14.765 5.434 9.246 10.779

kazakhstan 1.640 1.272 2.259 2.716 2.744 2.387 1.792 2.049

Korea 8.992 9.171 9.636 10.990 13.372 17.604 23.214 26.423 30.939 33.956 36.440 40.892 47.237 52.799 47.997 34.809 42.134 46.698

Kyrgyz 0.177 0.210 0.292 0.338 0.306 0.293 0.239 0.244

Malaysia 4.745 5.010 4.770 4.698 4.786 5.021 5.463 6.073 6.728 7.696 8.450 9.135 10.991 11.200 10.785 7.051 8.807 9.534

Nepal 0.235 0.221 0.240 0.239 0.266 0.296 0.329 0.305 0.298 0.279 0.307 0.324 0.391 0.406 0.431 0.425 0.447 0.486

newguinea 0.597 0.559 0.520 0.526 0.580 0.597 0.639 0.558 0.584 0.639 0.739 0.580 0.432 0.553 0.485 0.331 0.269

Pakistan 3.186 3.627 3.602 3.965 4.475 5.849 6.319 5.999 6.146 6.233 6.245 6.216 6.957 7.466 7.058 6.711 6.197 6.652

philippines 2.754 2.210 2.338 2.374 2.786 3.423 4.058 4.475 4.509 5.115 5.498 6.920 8.439 9.898 10.855 8.667 9.957 9.558

singapore 1.891 2.031 2.522 2.420 2.524 2.652 3.083 3.741 4.255 4.579 5.399 5.897 7.144 8.658 8.876 8.310 8.253 9.641

Srilanka 0.541 0.607 0.706 0.821 0.890 0.954 0.904 1.044 1.227 1.231 1.361 1.526 1.897 1.466 1.563 1.548 1.414 1.709

Taiwan 8.494 9.390 10.023 11.177 14.688 18.536 23.342 27.502 31.206 35.503 35.048 35.586 37.722 39.977 41.724 38.250 37.859 40.403

Thailand 5.156 5.503 5.262 5.497 5.724 6.197 6.879 8.025 9.057 11.032 12.480 14.091 16.698 18.608 15.276 12.401 13.844 14.088

Vanuatu 0.037 0.041 0.043 0.045 0.047 0.051 0.044 0.047 0.050 0.052 0.052 0.059 0.062 0.070 0.066 0.064 0.066

Vietnam 0.799 0.618 0.569 0.966 1.344 1.698 2.060 2.237 2.255 1.849 1.996

uzbekistan 1.405 2.264 3.084 3.020 3.076 3.522 2.659

Mean 6.271 6.498 6.552 6.875 7.465 8.186 9.388 9.546 9.924 10.617 10.896 10.696 12.288 13.678 14.093 13.166 14.488 15.837

3

Table 3: dGDP/dG for Developing Asian and Pacific Countries

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

azerbaijan 7.35 7.43 7.49 7.92 8.00 8.82 8.58 7.70 7.95

bangladesh 8.03 8.04 8.06 8.03 8.13 8.10 7.96 9.89 9.94 9.74 9.47 9.51 9.64 9.77 9.79 9.59 9.66 9.67

bhutan 6.82 6.85 6.88 6.95 7.10 7.11 7.08 7.11 7.00 7.01 6.97 7.08 7.15 7.19 7.24 7.28 7.31

cambodia 8.96 8.34 8.42 7.67 8.10 9.12 8.42 9.08 8.80 8.88 9.00 8.84 8.72

china 7.94 7.94 8.00 7.99 8.05 8.13 8.09 7.96 8.01 8.01 8.02 8.03 8.14 8.13 8.11 8.08 8.05 8.01

fiji 7.54 7.57 7.57 7.64 7.62 7.64 7.67 7.65 7.64 7.64 7.63 7.71 7.74 7.75 7.72 7.67 7.73 7.65

hongkong 8.61 8.72 8.68 8.70 8.87 8.91 8.81 8.71 8.63 8.54 8.54 8.52 8.44 8.45 8.47 8.34 8.27 8.33

india 8.27 8.23 8.17 8.10 8.07 8.09 8.10 8.13 8.15 8.17 8.18 8.25 8.19 8.22 8.15 8.09 8.03

indonesia 8.24 8.27 8.16 8.17 8.36 8.49 8.45 8.44 8.52 8.45 8.41 8.56 8.61 8.67 8.83 9.17 8.91 8.78

kazakhstan 7.93 8.19 7.96 8.01 8.05 8.19 8.20 8.14

korea 8.18 8.27 8.25 8.26 8.30 8.32 8.23 8.23 8.23 8.20 8.23 8.27 8.33 8.27 8.28 8.18 8.24 8.26

kyrgyz 7.50 7.57 7.60 7.65 7.68 7.65 7.59 7.60

malaysia 7.86 7.90 7.87 7.80 7.89 7.93 7.94 7.96 7.96 8.01 8.04 8.07 8.06 8.17 8.20 8.31 8.16 8.21

nepal 8.13 8.23 8.23 8.27 8.28 8.31 8.18 8.36 8.28 8.47 8.36 8.48 8.30 8.30 8.36 8.30 8.36 8.35

newguinea 7.56 7.55 7.54 7.58 7.59 7.61 7.58 7.57 7.60 7.62 7.63 7.79 7.79 7.67 7.66 7.62 7.63

pakistan 8.13 8.08 8.07 8.02 7.97 7.86 7.81 7.88 7.93 8.02 8.01 8.08 8.12 8.05 8.11 8.15 8.24 8.17

philippines 8.52 8.77 8.65 8.58 8.50 8.40 8.34 8.27 8.29 8.32 8.27 8.20 8.14 8.09 8.00 7.99 8.01 8.03

singapore 8.18 8.18 7.92 7.96 8.05 8.22 8.24 8.26 8.29 8.37 8.36 8.50 8.48 8.34 8.36 8.27 8.30 8.23

srilanka 8.15 8.18 8.03 7.95 7.92 7.92 7.97 7.97 7.94 8.00 7.98 7.99 7.89 8.20 8.23 8.29 8.39 8.21

taiwan 7.83 7.85 7.84 7.90 7.93 7.89 7.86 7.79 7.79 7.81 7.86 7.92 7.94 7.93 7.93 7.93 8.00 8.01

thailand 8.02 8.00 7.97 8.03 8.14 8.28 8.34 8.36 8.38 8.30 8.29 8.32 8.29 8.26 8.27 8.17 8.15 8.13

vanuatu 6.54 6.68 6.66 6.67 6.71 6.78 6.72 6.77 6.87 6.89 6.88 6.97 7.00 7.03 7.03 7.01 7.01

vietnam 8.02 8.51 9.10 8.68 8.51 8.53 8.50 8.54 8.64 8.94 8.95

uzbekistan 7.64 7.62 7.63 7.67 7.67 7.67 7.69

mean 7.92 7.96 7.92 7.92 7.97 8.05 7.98 8.09 8.08 8.10 8.08 8.09 8.12 8.13 8.18 8.17 8.14 8.26

1

References

Banker, R.D., A. Charnes, and W.W. Cooper, “Some models for estimating technical

And Scale efficiencies in data envelopment analysis”, Management Science, 30

(1984); 1078-1092.

Branson, Johannah and C.A. Knox Lovell, “Taxation and Economic Growth in New

Zealand,” in G.W. Scully and P.J. Caragata (eds.) Taxation and the Limits of

Government, (Boston: Kluwer Academic Publishers, 2000). 37-88.

Charnes, A, W.W. Cooper, and E. Rhodes, “Measuring the Efficiency of Decision

Making Units,” European Journal of Operational Research, 2 (1978); 429-444.

Debreu, G, “The Coefficient of Resource Utilization,” Econometrica 19 (1951), 273-92.

Farrell, M. J, “The Measurement of Productive Efficiency,” Journal of the Royal

Statistical Society Series A, General. 120 (1957), 253-81.

Leightner, Jonathan E. (2002), The Changing Effectiveness of Key Policy Tools in

Thailand, Final Report Submitted to East Asian Development Network, February

14, 2002.

Shephard, R. W., The Theory of Cost and Production Functions. (Princeton: Princeton

University Press, 1970).

2

Endnotes

1 Under PLS, an observation falls below the best practice frontier if unfavorable

omitted variables have affected that observation. This new interpretation is not inconsistent with the previous interpretation. Consider an analysis of the productivity of firms. In the previous interpretation, a firm that falls below (or to the right) of the frontier is inefficient. In the new interpretation, this inefficiency is due to omitted variables. For example, a firm may be inefficient because it has an inferior manager, because its workers have less education and/or less experience, because its capital is older and less productive, or because it functions in a less favorable environment. In other words, omitted variables explain why one observation is less efficient than another observation.

2. This is an output oriented DEA program because the output of each observation is compared to the output of observations with similar levels of inputs. Input oriented DEA programs are also commonly used. An input oriented DEA program compares the input usage of an observation to the input usage of other observations with similar levels of output. Technically, either an output or input oriented DEA program could be used for TPLS. However, for the simulations run for Leightner (2002), an input oriented DEA program resulted in much more severe end-grain problems. 3 Error can come from one of three sources -- imprecise measurement, rounding off, and/or omitted variables. TPLS eliminates the error from omitted variables. The remaining error, due to imprecise measurement or rounding off, should be relatively small. The error included in Y2 is probably larger than what can reasonably be attributed to imprecise measurement and rounding off for most empirical studies since it is constructed as one tenth of a series similar to the independent variables. 4 The OLS estimate is 153.06. The PLS estimate is 155.34. The TPLS estimate is 154.54. 5 The end grain observations and the remaining observations after the last TPLS run will not have estimated TPLS coefficients. 6 These rules were developed by a trial and error method of seeing which rules appear to work best. Additional research needs to be conducted to determine what rules make RTPLS perform optimally. Such tests are beyond the scope of this paper. 7 Note: OLS produces one estimate which is suppose to fit all the observations; in contrast, RTPLS produces a unique estimate for each observation. The ratio results that follow do not include RTPLS estimates for the three percent of the observations with the smallest independent variable (the one not omitted) because Leightner (2002) found that these observations tended to produce much greater RTPLS errors. Leightner recommends that RTPLS estimates for these observations not be made or that RTPLS

3

estimates for these observations be clearly labeled as more suspect. 8 Here, and else where, size refers to the relative size of GDP as expressed in US dollars. Size does not refer to physical size. 9 Leightner (2002) found that the RTPLS estimates for the 3 percent of the observations that have the smallest values for the included independent variable are more suspect than the RTPLS estimates for other observations. These more suspect estimates are for Bhutan in 1983, 1984, 1985, 1990, 1991, and 1993 and for Vanuatu in 1983-1986 and in 1989. 10 Between 1989 and 1990, Bangladesh’s dGDP/dG changed much more than any other country’s (in a distant second and third to Bangladesh, Vietnam and Cambodia’s estimates of dGDP/dG varied the most between 1990 and 1993). Furthermore, after 1990, Bangladesh enjoyed the highest estimated multipliers for dGDP/dG. To test the robustness of my estimates, I redid the analysis after eliminating Bangladesh. On average, the dGDP/dG estimates were 0.105 lower when Bangladesh was not included. Thus including Bangladesh only changed the results on average by 1.3 percent (0.105/8.074). However, there were some patterns in how the results changed over time and countries when Bangladesh was omitted. Average dGDP/dG went down a greater amount in earlier years than it did in latter years. In temporal order (from 1983 to 2000), dGDP/dG when Bangladesh was included minus dGDP/dG when Bangladesh was excluded was 0.18, 0.15, 0.18, 0.17, 0.14, 0.10, 0.13, 0.13, 0.13, 0.12, 0.11, 0.10, 0.08, 0.08, 0.05, 0.05, 0.07, -0.005. The countries who had dGDP/dG most affected by omitting Bangladesh were Vanuatu (average dGDP/dG fell by 0.96), Bhutan (average dGDP/dG fell by 0.83), Kyrgyz (average dGDP/dG fell by 0.35), Fiji (average dGDP/dG fell by 0.32), New Guinea (average dGDP/dG fell by 0.32), Uzbekistan (average dGDP/dG fell by 0.28), Vietnam (average dGDP/dG rose by 0.26), and Hong Kong (average dGDP/dG rose by 0.24). Remember that the estimates for the three percent of the observations with the smallest values for the independent variable are more suspect (Leightner, 2002). It is interesting to note that the countries most affected by omitting Bangladesh are the countries that contain the three percent of the observations with the smallest value for the independent variable – Vanuatu and Bhutan. 11 Traditional methods that use dummy variables and/or that modeled interactions can produce varying estimates for dGDP/dG, but this is not normally done. Furthermore, it is almost impossible to know how to perfectly specify a model of the whole economy when data is not infinite. When using traditional methods, it is possible that one mis-specified equation can drastically bias the resulting estimates of dGDP/dG. RTPLS does not carry these same problems since a system of equations does not have to be constructed to use RTPLS.