Chapter 16: Empirical Evidence on Demand, Supply and
Surpluses
16.1: Introduction
This chapter shows that the theoretical material that we have been studying has empirical relevance.
We apply the theory to the estimation of a demand and supply system for some commodity. We are
searching for a specification that has both theoretical justification and fits the facts - is empirically
relevant. If you want, you can reproduce what we have done here with other commodities.
We should warn you that this chapter assumes some basic familiarity with basic econometrics particularly the concept of a regression. If you have not yet done any econometrics, full
understanding of this chapter may have to wait until later. I thought about including some material
on econometric pre-requisites, but decided on the grounds that such material would take up too
much space. There is however a glossary of key terms at the end of the chapter. If you really have
not done any basic regression analysis before, I would suggest that you reserve this chapter for a
later date, and take on faith the important message: that the theory we are presenting in this book
does have empirical relevance and is useful. I should note that nothing in the rest of the book relies
on you understanding (or even having read) this chapter.
16.2: The data to be explained
The data that we are using is reproduced at the end of this chapter.
We choose a commodity that is important and interesting - the demand for and supply of food in the
UK. We need to start with some data. This we obtained from the publication Economic Trends
Annual Supplement (ETAS). (Actually the data was downloaded electronically from the UK Data
Archive which is located at the University of Essex, but the data is also available in printed format
in ETAS.) If you look in that publication there are two series for Household Expenditure on Food one series in current prices (code name in ETAS: CCDW) and the other a series in constant 1995
prices (code name CCBM). The first of these is money expenditure while the second corrects for
price changes. So it is the latter that is the indicator of the quantity of food purchased. We shall call
this variable RFOD - standing for Real expenditure on FOOD. We shall call the variable giving
the expenditure on food in current prices NFOD – standing for Nominal expenditure on FOOD.
You will find the data on these variables in the table at the end of this chapter – in the 5th and 6th
columns of that table.
From these two series we can derive the Price of FOOD - which we denote by PFOD – we do this
by dividing the series of expenditure on food in current prices by the series of expenditure on food
in constant prices. Thus PFOD = NFOD/RFOD. There is data available from 1948 to 1999 - a
total of 52 observations. If we draw a scatter diagram of price (PFOD) against quantity (RFOD) we get figure 16.1.
We should note that this is annual data and that each cross represents the price and quantity of food
purchased in a particular year. There are 52 observations and hence 52 crosses. The figure looks a
little like a supply curve.
Note, however, that we have done something odd - since all prices are rising through time we ought
to correct the price series for the general movement in prices. We can do this by first obtaining data
on overall prices. We do this by taking the series for the total household expenditure in current
prices (code name ABPB) - which we shall call NALL (Nominal expenditure on ALL
commodities) and dividing it by the total household expenditure in constant prices (code name
ABPF) - which we shall call RALL (Real expenditure on ALL commodities). The data on these
variables is in the 3rd and 4th columns of the table at the end of this chapter. Dividing NALL by
RALL gives us PALL - the Price of ALL commodities. Thus PALL = NALL/RALL. We can
then find the relative price of food - PFOD/PALL. Graphed against the quantity of food purchased
over the period from 1948 to 1999 we get the scatter diagram in figure 16.2. Again there are 52
crosses – one for each year.
16.3: The demand for food in the UK
Figure 16.2 looks like a demand curve. It looks vaguely linear and perhaps a linear demand curve
would be a good fit. But we should think about the theory that we have been studying. Clearly we
can reject the hypothesis that food is a perfect substitute for other commodities (you should ask
yourself why) and that food is a perfect complement with other commodities (again you should ask
yourself why). Let us try Cobb-Douglas preferences. You will recall that this is particularly simple:
it states that the amount spend on a commodity is a constant fraction of income. This means that
RFOD should be a constant fraction of NALL/PFOD. That is, real expenditure on food should be a
constant fraction of the real income (or real total expenditure). Here, for simplicity, we are
assuming that the decision taken by the consumer is how to decide the allocation of total
consumption over the various commodities - we are taking out the saving decision, which we have
not yet studied. If we do a regression of RFOD against NALL/PFOD we get the following:
RFOD = 0.146 NALL/PFOD + u
(21.0)
log-likelihood = -568.056
This is the equation of the ‘best-fitting’ straight line to the scatter produced by plotting RFOD
against NALL/PFOD. You should note that this is not figure 16.2, but you could draw the scatter
diagram yourself using the data in the appendix and inserting on the graph the line above.
The term in brackets under the coefficient is the t-ratio. The coefficient is clearly significantly
different from zero. This coefficient (on NALL/PFOD) indicates that consumers on average spend
14.6% of their total consumption expenditure on food. This is much higher than is actually the case
(in 1999 the proportion was less than 10%) - which suggests that the specification is not particularly
good. Actually a more direct test of the hypothesis that preferences are Cobb-Douglas can be found
by simply looking at the proportion of total expenditure that goes on food: this started out at almost
30% in 1950 but was less than 10% in 1999 – a clear rejection of the Cobb-Douglas specification.
The log-likelihood is a measure of the goodness of fit of the equation. The fit is quite good.
However it will become clear that other specifications fit the data better. One possible contender is
the Stone-Geary Utility function which we know (see equation 7.3 in chapter 7) leads to a demand
function of the form:
q1 = s1 + a (m – p1s1 – p2s2)/p1
where good 1 is the good of interest (in this case food) and good 2 is all other goods. Let us denote
the price of all other goods by QFOD ( which is simply given by (NALL-NFOD)/(RALL-RFOD).
Then we can conclude that the Stone-Geary demand function for food is such that RFOD is a linear
function of NALL/PFOD and QFOD/PFOD. (That is, using the original notation q1 is a linear
function of m/p1 and p2/p1.) If we fit the data to this function we get the following result:
RFOD = 44491 + 0.065 NALL/PFOD - 23426 QFOD/PFOD + u
(11.4) (10.8)
(3.6)
log-likelihood = -446.349 R-squared = .94254 residual sum of squares = 86,932,642
The numbers in brackets under the coefficients are the corresponding t-ratios. They clearly are all
significant. The implied subsistence level of expenditure on food is £44,491m - equivalent to
around £800 per head per year in 1995 prices. The coefficient on the variable NALL/PFOD
indicates that once the subsistence levels of both food and other commodities have been bought,
consumers on average spend 6.5% of an extra income on food. This seems more reasonable. The
log-likelihood of this equation is significantly higher than that for the Cobb-Douglas specification,
and the R-squared indicates that 94.2% of the variation in expenditure on food is explained by this
Stone-Geary specification. This specification therefore seems reasonable on econometric grounds1
and on economic grounds.
16.4: Simultaneous bias
At this stage we ought to recognise an important fact. The data that we have got on expenditure on
food is not just demand data. It is generated by the simultaneous interaction of demand and supply.
What effect does this have? We cannot give a full explanation here - a full explanation requires a
course in econometrics - but we can explain the nature of the problem.
As we have already said, the data that we have results from the interaction of demand with supply.
If the demand and supply functions have remained stable throughout the observation period, that
must mean that there is only one intersection point - and so we would observe just one value for
RFOD and just one value for the price PFOD. As it happens we have lots of different observations
- as figures 16.1 and 16.2 make clear. This must imply that one or both of the demand and supply
schedules must have moved during the observation period. Let us consider what might have
happened.
Suppose just the demand schedule has moved. We would have something like figure 16.3.
Notice where the intersection points lie - all along the supply curve! All we can observe from the
data is the supply curve. (Notice that we can deduce nothing about the demand curves - just
consider a second family of demand curves with slopes different from those above.)
If however it was just the supply curve that had moved - we would have something like figure 16.4.
1
We appreciate that econometricians would want to do some further tests of the specification. However such tests are
beyond the scope of the book and may require us to bring in some further economic theory. The crucial point is that we
have a specification that comes from some economic theory and is econometrically respectable.
Here we would just be able to observe the demand curve.
Now we know something from economic theory - we know that changes in income (or changes in
the total expenditure) will shift the demand curve and we know that changes in factor prices will
shift the supply curve. If we look at data on these variables over the period we are considering we
will see that all these variables have indeed changed over the period. So both the demand and
supply curve have shifted. If we ignore this information we are going to get biases in our
estimation. Going back to the demand curve estimated above, we should recognise that some of the
movements must have resulted from shifts in the supply curve.
To explain how we eliminate these biases caused by the simultaneous determination of price and
quantity takes us deep into econometrics - and we cannot discuss these issues here. Suffice it to say
that if we use a method of estimation called Instrumental Variables Estimation (as distinct from
Ordinary Least Squares Estimation – which we used above) we can get rid of the bias.
Let us report the results of instrumental variables estimation of the demand equation. This method
takes into account that the price variable on the right hand side of the equation is partly determined
by the variables which enter the supply equation - namely factor prices. Instrumental variables
estimation (using the factor prices - which we will discuss later - as instrumental variables) yields
the following estimate of the Stone-Geary demand function for food:
RFOD = 41962 + 0.049 NALL/PFOD - 14210 QFOD/PFOD + u
(8.5)
(5.9)
(1.6)
residual sum of squares = 4,450,094
DEMAND EQUATION
The subsistence level of food expenditure is now £41,962 m in 1995 prices. The proportion of extra
income spent on food is 4.9%. You will notice changes in the estimates as a result of the elimination
of simultaneous bias through the use of the instrumental variables estimation technique. Given the
fact that instrumental variables estimation is a consistent method of estimation while ordinary least
squares is not (in the context of a simultaneous system) we take the equation above as out estimate
of the demand curve for food in the UK.
16.5: The supply of food in the UK
We assume a Cobb-Douglas production function and that the food production industry is
competitive. We know from the chapters on cost curves that the cost function for a two-input CobbDouglas is proportional to (see equation (12.1))
y1/(a+b) w1a/(a+b) w2b/(a+b)
It follows that the marginal cost function for a firm or an industry with decreasing returns to scale is
proportional to
y(1-a-b)/(a+b) w1a/(a+b) w2b/(a+b)
If we now use the profit maximising condition that price should equal marginal cost and if we solve
that equation for the implied optimal output we find that it is given by (where k is some constant)
y = k p(a+b)/(1-a-b) w1-a/(1-a-b) w2-b/(1-a-b)
This is the supply function for a two-input competitive industry with Cobb-Douglas technology. As
most of the econometric packages like linear equations, we linearise it by taking logarithms. We
get:
log(y) = constant + [(a+b) log(p) – a log(w1) – b log(w2)]/(1-a-b)
This is a linear equation in the variables log(y), log(p), log(w1) and log(w2). You will notice that the
price of food has a positive coefficient while the input prices all have negative coefficients.
Obviously if there are more than 2 factors of production the equation can be generalised
appropriately
We now need to find some appropriate data. We already have the price of food - PFOD. We restrict
attention to variables that can be easily found in Economic Trends Annual Supplement.
There are three obvious factors of production - labour, capital and raw materials and fuels. We take
as our indicator of the wage rate the variable (code name LNNK in ETAS) Unit Wage Costs in the
whole economy (there is no data specifically for the food-producing industry). We call this PUW.
We take as our indicator of the cost of capital the Interest rate on long-term government securities.
This has the ETAS code AJLX and we call it NLI (the Nominal Long term rate of Interest). Finally,
recognising that the food industry has to buy materials and fuel as input we take the price index for
raw materials and fuels purchased by manufacturing industry (there is no variable specifically for
the food industry). This has ETAS code PLKW and we call it PMAF. The data are listed in the 2nd,
9th and 10th columns of the table at the end of this chapter. Our hypothesis is that the log of RFOD
is a linear function of the log of PFOD, the log of PMAF, the log of NLI and the log of PUW. If
we carry out an instrumental variables estimation of this equation (again to avoid bias caused by
simultaneity) we obtain
log(RFOD)= 13.68 + 0.761 log(PFOD) - 0.0948 log (PMAF) - 0.0934 log(NLI) - 0.485 log(PUW)
(13.9) (3.3)
(1.2)
(2.0)
(2.1)
Residual sum of squares = 0.0102
t-ratios in brackets
SUPPLY EQUATION
This is our estimated supply equation. You will see that all the coefficients have the right sign and
are significant - except the coefficient on log(PMAF). We left this in as the ordinary least squares
estimation suggested that it was important. For the record the ordinary least squares estimate is
reported below:
log(RFOD)= 11.98 + 0.348 log(PFOD) - 0.148 log (PMAF) - 0.0696 log(NLI) - 0.0786 log(PUW)
(23.5) (3.1)
(2.5)
(2.0)
(0.6)
Residual sum of squares = 0.0056
t-ratios in brackets.
You might like to disentangle the coefficients of the underlying Cobb-Douglas production function.
16.6: An investigation of the effect of a tax on food
At the moment food is exempt from VAT. Suppose the government were considering the
imposition of VAT. Let us examine here what would happen.
The initial situation is given by the demand and supply equations above. Let us take the position as
in 1999 - the latest year for which data is available. In this year we have the following values for the
exogenous variables:
NALL = 564368
PALL = 1.10043 PMAF = 83.7 NLI = 4.7 PUW = 115 QFOD = 1.10621
If we substitute these values in the demand and supply equations and then graph the demand and
supply equations we get figure 16.5.
You will see that the initial equilibrium - a value for RFOD of 52832 and a value for PFOD of
1.076 - is very close to the 1999 outturn - a value for RFOD of 52277 and a value for PFOD of
1.105. The reason that they are not exactly equal is simply that the fitted demand and supply curves
do not fit exactly.
Now consider the introduction of a tax - let us say of 10%. We will see2 in chapter 27 that this
drives a wedge - equal to 10% of the selling price between the demand and supply curves. The new
equilibrium is as in figure 16.6.
The new equilibrium price that the sellers receive is the lower price - which is 1.055 - and the new
equilibrium price paid by the buyers is the upper price - which is 1.160. This latter is 10% more
than the former. The government takes the difference - 0.1055 - on each unit of the good sold. In
this new equilibrium the quantity exchanged is 52042 - a reduction of some 1.5%. This is a
relatively modest fall - because the demand is very insensitive to the price, as one would expect
with a commodity like food. For the same reason, it is the buyers who largely pay the tax - the
price they pay rises from 1.076 to 1.160 - an increase of around 7.8%. The sellers on the other hand
see a fall in the price that they receive - from 1.076 to 1.055 - a fall of 1.98%.
We can also calculate what happens to the surpluses of the buyers and sellers. Consider figure 16.7.
2
This material anticipates somewhat the material of chapter 27. You may find it helpful to have a quick glance at
chapter 27 before proceeding further with this chapter.
The buyers lose the surplus bounded by the old price, the new price and the demand curve. (Be
careful - the graph does not go to zero at the left-hand axis.) This area is approximately equal to
(1.160-1.076) times (52042+52832)/2 which is 4405. We can calculate it exactly by finding the area
by integration - the exact figure for the loss in consumer surplus is £4,423m - assuming 55 million
people in the UK this is equivalent to £80 per head at 1995 prices.
The loss in producer surplus is the area bounded by the old price, the new price received by the
sellers and the supply curve. This area is approximately equal to (1.076-1.055) times
(52042+52832)/2 which is 1101. Again we can calculate it exactly by integration - the exact figure
for the loss in producer surplus is £1,106m in 1995 prices. The combined loss of surpluses is
£5,529 at 1995 prices.
The government takes the tax - 0.0155 on each of the 52042 units exchanged - this is £5,488 at
1995 prices. The difference between this and the combined loss of surpluses - £41m at 1995 prices is the deadweight loss of the tax - a concept we shall discuss in chapter 27. It is equal to the little
triangle bounded by the supply curve, the demand curve and the vertical line at the new quantity.
The deadweight loss is relatively small because the demand curve is rather insensitive to the price.
16.7: Summary
We have shown how the theoretical material we have been developing is useful in a practical policy
problem. We have:
estimated a demand curve using both economic theory and econometrics;
estimated a supply curve using both economic theory and econometrics;
mentioned the econometric problems that arise when we have a simultaneous system;
used the estimated demand and supply system to work out the implications of the imposition of a
new tax.
16.8: Glossary of Technical Terms
A complete treatment of the econometric issues involved in this chapter are beyond the scope of this
book. You may like to refer to some standard econometric text if you want further details. A good
text, which explains the key terms clearly is Kennedy, P., "A Guide to Econometrics", Blackwell,
4th Edition, 1998. Here we provide a verbal summary of some of the key terms used in this
chapter.
We start with a scatter diagram which is the type of graph illustrated in figures 16.1 and 16.2. This
is simply a graph of one variable against another, where the points graphed are the observations on
those variables. So, if we have 52 observations, we have 52 points – one for each observation. This
is a two-dimensional scatter diagram. The regression line fitted to this scatter diagram is the ‘bestfitting’ straight line which approximates the scatter. There are various definitions of what is meant
by ‘best-fitting’. In a simple ordinary least squares regression the criterion of ‘best-fitting’ used is
the minimisation of the sum of squared distances from the points to the line.
Clearly in general the regression line does not fit the observations exactly (unless the observations
happen to lie exactly along a straight line – which is not the case with our scatter diagrams). It is
useful to be able to report how closely the line fits the observations – or how well the line ‘explains’
the observations. There are various measures of goodness of fit - the most common one being
called R2 – which measures the proportion of the variance of the data explained by the straight line.
A value of R2 = 1 means that the line ‘explains’ the data exactly, while a value of R2 = 0 means that
it does not ‘explain’ it at all3. The better the fit, the higher the value of R2. An alternative measure
is the log-likelihood, which is too complicated to explain simply. But again, the higher the value of
the log-likelihood, the better the fit.
The coefficients of the regression line are the estimates of the coefficients of the theoretical
equation we are estimating: the coefficients are estimates of the theoretical coefficients. Clearly if
the regression line does not fit the observations exactly the estimates will not equal the theoretical
coefficients. There will be some margin of error associated with these estimates. The standard error
of the estimate is a measure of this error. The smaller the standard error the more precise is the
estimate. We can use these standard errors to test the proposition that the theoretical coefficients
are zero. We do this by dividing the estimate by its standard error to form what is known as the tratio of that coefficient. If this t-ratio is ‘big enough’ we can reject the proposition that the
theoretical coefficient is zero. What is meant by ‘big enough’ depends upon the context, but as a
rough rule of thumb, a t-ratio larger than 2 is big enough. In this case we say that the estimated
coefficient is significantly different from zero.
All of this material can be generalised to the estimation of a function of more than one variable,
though it is difficult to portray it graphically. In particular we can generalise the idea of the ‘bestfitting’ function to a function of more that one variable. The ‘best-fitting’ criterion that we defined
above – minimising the sum of squared distances from the points to the line – is defined as ordinary
least squares. Under certain assumptions about the generating process, it can be shown that this is
the best way of estimating the theoretical coefficients. These assumptions will be true, in particular,
if the independent variable(s) in the regression line are truly independent. If they are not, then the
method of ordinary least squares may produce estimates that are biased (that is, are not on average
equal to the theoretical coefficients) and even inconsistent (that is, do not approach the theoretical
coefficients even with an infinite number of observations). In such cases other fitting methods may
be better. In the context of the demand and supply estimation that we have done, ordinary least
squares fitting is appropriate if price (the independent variable) is truly independent. But we know
that the price is the solution to the interaction of supply and demand and therefore cannot be truly
independent of demand. Thus some other fitting method is appropriate – one that takes into account
the fact that price is not independent. One such method is that of instrumental variables estimation
as used in this chapter. It uses truly independent variables to estimate the demand and supply
equations. An explanation can not be provided here – as such issues occupy large parts of
econometric texts. However, Kennedy (cited above) provides a good explanation.
3
We put the word ‘explain’ in quotation marks as this is merely a statistical – not a theoretical – explanation.
Appendix: Data and data sources
YEAR
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
,
NLI
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
5.30
5.80
6.43
6.91
6.80
7.54
9.05
9.21
8.85
8.90
10.71
14.77
14.39
14.43
12.73
12.47
12.99
13.78
14.74
12.88
10.80
10.69
10.62
9.87
9.47
9.36
9.58
11.08
9.92
9.12
7.87
8.05
8.26
8.10
7.09
5.45
4.70
NALL
8417
8771
9257
9998
10526
11226
11906
12832
13494
14227
15013
15802
16573
17422
18438
19565
20868
22151
23391
24579
26451
28054
30547
34250
38780
44360
51126
62881
73060
83504
96368
114458
132663
147120
160997
176881
189244
206600
228848
251143
283425
310493
336492
357785
377147
399108
419262
438453
467841
498307
530851
564369
RALL
142958
145251
149082
147049
147017
153393
159716
166245
167041
170434
175182
182697
189586
193663
197837
206304
212644
215002
218707
223851
230135
231201
237739
245429
261277
275705
271228
270421
271477
270434
284901
297453
297256
297237
299810
313648
319357
331404
353831
372601
400427
413498
415788
408309
410026
420081
431462
438453
454686
472701
491378
512864
RFOD
32737
33977
35572
34938
30760
32533
33210
34385
34941
35466
35893
36580
37366
37985
38366
38568
39041
39016
39445
40094
40303
40418
40824
40861
40789
41770
41038
41050
41484
41126
41879
42812
42866
42591
42694
43416
42676
43213
44572
45709
46745
47538
47055
47114
47664
48282
48931
49274
50931
51786
51627
52277
NFOD
2320
2508
2758
3022
2824
3122
3295
3585
3787
3928
4028
4157
4225
4366
4560
4689
4889
5059
5297
5485
5696
6035
6429
7105
7614
8751
10028
12313
14459
16596
18373
20988
23655
24946
26490
28061
29274
30657
32574
34402
36491
39143
41817
44044
45193
46334
47122
49274
52513
53188
53789
54862
PALL
0.0589
0.0604
0.0621
0.0680
0.0716
0.0732
0.0745
0.0772
0.0808
0.0834
0.0856
0.0864
0.0874
0.0899
0.0931
0.0948
0.0981
0.1030
0.1069
0.1098
0.1149
0.1213
0.1284
0.1395
0.1484
0.1608
0.1884
0.2325
0.2691
0.3087
0.3382
0.3847
0.4462
0.4949
0.5369
0.5639
0.5925
0.6234
0.6467
0.6740
0.7078
0.7508
0.8092
0.8762
0.9198
0.9500
0.9717
1.0000
1.0289
1.0541
1.0803
1.1004
PFOD
0.0708
0.0738
0.0775
0.0864
0.0918
0.0959
0.0992
0.1042
0.1083
0.1107
0.1122
0.1136
0.1130
0.1149
0.1188
0.1215
0.1252
0.1296
0.1342
0.1368
0.1413
0.1493
0.1574
0.1738
0.1866
0.2095
0.2443
0.2999
0.3485
0.4035
0.4387
0.4902
0.5518
0.5857
0.6204
0.6463
0.6859
0.7094
0.7308
0.7523
0.7806
0.8234
0.8886
0.9348
0.9481
0.9596
0.9630
1.0000
1.0310
1.0270
1.0418
1.0494
All data from Economic Trends Annual Supplement. Details follow.
PMAF
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
32.0
35.3
44.3
50.5
50.5
59.0
69.3
78.5
83.4
88.1
96.6
96.6
81.0
82.6
84.5
89.1
88.5
86.6
86.3
90.2
91.9
100.0
98.8
90.6
82.5
83.7
PUW
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
43.4
53.0
58.2
66.7
67.7
70.0
74.0
76.9
78.6
80.8
84.8
90.4
94.8
95.0
94.8
95.3
100.0
105.4
109.2
114.6
115.0
RAW SERIES
ABPB Household Expenditure:Total Household Final Consumption Expenditure: CP NALL
ABPF Household Expenditure:Total Household Final Consumption Expenditure: KP95 RALL
CCBMHousehold Expenditure: Household exp.on food: KP95
CCDWHousehold Expenditure: Household expenditure on food: Current price
RFOD
NFOD
AJLX BGS : long-dated (20 years) : Par yield - per cent per annum
NLI
LNNK UWC : whole economy SA: Index 1995=100: UK
PUW
PLKW PPI: 6292000000: M & F purchased by manufacturing industry
PMAF
DERIVED SERIES
Price of Final Consumption Expenditure
Price of Food Expenditure
Price of Non-Food Expenditure
NALL/RALL
NFOD/RFOD
(NALL-NFOD)/(RALL-RFOD)
VALUES OF VARIABLES IN 1999
NALL
PALL
PMAF
NLI
PUW
PFOD
RFOD
QFOD
564369
1.10043
83.7
4.7
115
1.104945
52277
1.106
PALL
PFOD
QFOD