The effect of immigrants on natives' incomes through the use of capital

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FACULTY WORKING
PAPER NO. 873

The Effect of Immigrants on Natives' Incomes
Through the Use of Capital

siulian L Simon
A. James Heins

IHE UBRARV OF THE
S?'.riS?(TypFILUNOIS

College of Commerce and Business Administration
Bureau of Eccnonic and Business Researcn
University' of Illinois. Urb&na-Chanpaign

;l;:i:;li^lilllifii

BEBR

FACULTY WORKING PAPER NO. 873
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
June 1982

DepartD

The person charp-inp- th;.

sponsible for its rif ^ material is re-

-^■•ch it .as;; thT;wn°o''''^^fro"

iicomes

I Economics

Abstract

This paper deals with questions about the effects of immigrants on
three types of capital: the private capital immigrants work with, the
public (government) capital that immigrant workers use, and the public
capital used for services by immigrants.

Private capital dilution is unimportant. The overall effect is
perhaps 1 percent or 2 percent, small enough to ignore.

In the government sector, workers can be assumed to obtain all the
returns to capital, and about 8 percent of immigrants work in this
sector. Therefore, for productive capital taken altogether, we estimate
that immigrants capture the returns from only 8 percent of the capital
they work with, the government capital; the result is a loss of perhaps
2 percent of an immigrant family's income for one year, which is about
the same magnitude as the gain to natives through the private capital
that immigrants work with.

The cost to natives of equipping an immigrant family with
"demographic capital" — schools, hospitals, and local roads — turns
out to be much more important. This quantity depends upon the cost of
such equipment, the proportion financed by bonds, the average length of
life of the capital, and the average life of the bonds. We develop an
estimating equation, and calculate that the cost to natives in 1975
dollars is $4172, about a fifth of a year's income for an average
family. This is not insignificant in magnitude. But this amount —
together with the effect through productive capital dilution discussed
in the first part of the paper — is considerably smaller than the
benefits of immigrants to natives through their relatively low use of
welfare services and their relatively high contribution of taxes.

■1 -I

*.'.

:i' ; 1

j •..:-■»

THE EFFECT OF IMMIGRANTS ON NATIVES' INCOMES THROUGH THE USE OF CAPITAL
Julian L. Simon and A. James Heins*

INTRODUCTION

Immigrants are a bad deal for natives because they obtain benefits
from capital they do not pay for, according to Usher (1977). Usher
reached this conclusion for the U.K. by applying the concept of capital-
returns capture developed by Borts and Stein (1966) , and by Berry and
Soligo (1969) B-S-B-S hereafter. The same conclusion would surely follow
for the U.S. and other developed countries if one followed Usher's method.

This paper criticizes Usher's method of applying the capital returns
concept, and proposes a new approach. This is also a criticism of Simon's
earlier inadequate use of the same concept in the context of Russian
Jewish immigrants into Israel (1976). The approach offered here leads
to a less negative partial assessment of the effects of immigrants on
native's incomes in the U.S. by way of the returns to capital than did the
previous work.**

A key element in this approach is separating the analysis of "pro-
duction" capital used on the job by immigrants from "demographic consumption"

*We appreciate comments from Warren Sanderson, Oded Stark,
Dan Usher, and a Hoover Institution seminar group.

**For perspective we should note that the effects through capital
use are only a small part of the overall impact of immigrants upon
natives. Elsewhere one of us shows (Simon, 1981) that the net balance
of transfer payments and taxes is positive and outweighs the negative
capital-returns aspect of the immigrant native's relationship to natives
that we shall find here, leading to a positive net effect of immigrants'
effect on natives, even without including the positive effect of immi-
grants upon productivity.

-2-

capital used in such services as schooling and medical care. Within the
production capital analysis, a key element is distinguishing the effects
in the private and public sectors. And with respect to demographic capital,
a key element is recognizing that the benefits which immigrants obtain from
existing public capital are irrelevant unless there is a congestion effect,
because the existing capital's cost is sunk and largely has a public-goods
character. This approach allows us to avoid difficult issues, including
the interpretation of corporate taxes, which are present in Usher's and
Simon's earlier approach.

THE SIZE OF THE CAPITAL-RETURNS-CAPTURE EFFECT*
Estimating satisfactorily the amount of the capture of returns to
capital by immigrants requires that we be very careful about our aim.
We must agree that the main subject of inquiry is the creation of addi-
tional output by the immigrant, and its effect on natives. It is vital to
recognize that the effect of this additional output upon the immigrant
himself /herself is not part of the inquiry; Usher (1977) implicitly did not
see it that way, nor did Simon earlier (1976), and therefore those papers
simply estimated the proportion of the total capital in the society from
which immigrants might receive returns either because the capital is
owned privately or because of corporate and other taxes in the returns
to capital. And of course the effect on the persons remaining in the
land of emigration is not part of the subject here.

^Capture of capital returns" means simply the receipt of payments
made to owners of private productive capital through dividends, interest
and rent.

-3-

Let us begin (adopting Usher's notation, diagram and general
approach for comparability) by noticing that the output with an im-
migrant (Q + AQ) , just as output without the immigrant (Q) , is divided
among three types of recipients — the immigrant employee, the owner of
the industrial capital, and the "government."

(1) Q = Q + Q = wL + rK + Q (=T)
P g P P g

Q+AO=Q +AQ +Q +AQ = (w+Aw) (L +AL ) + (r+Ar) (K +AK ) + (T+AT)
PPgg PP PP

where Q = native output

p = the private sector

g = the government sector

w = the wage level without immigrants

L = labor force without immigrants

r = after-tax rate of return to capital without immigrants

K = capital stock without immigrants

T = total taxes without immigrants

A = an incremental quantity, the difference between the
situation with immigrants compared to the situation
without immigrants.

We define private capital's "share" as what owners of capital receive
after taxes. It would not seem sensible to discuss whether the taxes
paid to government — corporate and "indirect" — come out of "capital's
full share" or not; no definition of "capital's full share" would seem
to make sense here, as consideration of these two notions shows: (1)
No economist would like to argue that "capital's full share" is "capital's
just share." (2) The share of the output that capital would receive if

-4-

govemment took no taxes is not obviously different (to a first approxima-
tion) from the share that capital receives after taxes, because we can
assume that capital owners will bid up to their margins for the immigrant's
services, and their marginal calculations will include the tax effects of
hiring the immigrant. So there is little reason to argue that the share
that capital actually receives is different than an ideal "capital's share"
or "capital's full share."

Focusing now on the private sector, if capital's share is what it
receives, then the only way that an immigrant working in the private
sector can receive some part of the additional private product (AQ )
other than his own marginal product is through corporate tax payments.
Therefore, we must inquire into the nature of the additional corporate
taxes paid (AT ) due to the immigrant's arrival and consequent addi-
tional outputs.

The total additional taxes (AT) following on the immigrant's entry

at least balance the additional expenditures (e.g., on schooling and

transfer payments) that occur because of the immigrant. (Simon's recent

work, 1981, finds that immigrant families pay distinctly more in taxes

than they receive in services, largely because of their age composition).

There seems no reason not to think of the corporate taxes that go toward

the extra services for immigrants being in the same proportion to total

taxes as they are for all persons ' services . That is , AT >_ AG and

AT T

— =E. = — 2-. If so, there is certainly no loss to natives by way of

corporate taxes, that is, AT is at least as large as the cost of any

services to immigrants that it might be expected to cover.

-5-

Some of the additional corporate tax^ payments may be thought of as
rent on publicly-owned capital used by the corporation, e.g., roads and
dams. And part of this rent may be gained by immigrants, in similar pro-
portion to other citizens. But what matters here is the effect on
natives. And the amount of such "rent" obtained by natives is likely
to be of a small order of magnitude, by any test, and hence we shall
ignore it for convenience (though noting that excluding this factor
reduces the apparent benefit of immigrants on natives, because we are
ignoring a flow that benefits natives).

The argument so far adds up to the fact that since AT >_ AQ , which
allows us to say that AT = AQ and T = Q , we can rewrite (1) as

(la) Q^ = wL + rK
P P P

Q + AQ = (w+Aw)(L +AL ) + (r+Ar) (K +AK ).
P P P P P P

If all immigrants worked in the private sector, and we could therefore
treat the government sector simply as if it were a foreign company that
sells inputs to the private sector, the B-S-B-S analysis would now follow
without further ado; immigrants would benefit natives as a whole by the
celebrated "triangle" in Figure 1.

But some immigrants work for the government. In that sector there
are no returns to capital that natives capture but the immigrant in
question does not. A key magnitude then, is the proportion of immigrants
that work for the government. This must be compared to the gain from
the "triangle" in order to calculate an overall assessment of the impacts
of immigrants through their involvement with the capital used in production.

MARGINAL
PRODUCT

OF
LABOUR

w+Aw

I/2ALAW

(w+Aw)L

LABOUR
FORCE

-6-

Calculation of the Capture of Capital Returns

Let us begin by taking notice, as Usher demonstrated by expanding
(la) in a Taylor series, that the "triangle" of additional returns to
the owners of private capital is small when the immigration is realis-
tically small; in the context of Usher's Cobb-Douglas production func-
tion example the gain is about 1/219 of the loss in labor income to
natives. And in a simulation (1976) Simon found that a flow to immigrants
of less than a 2% share of the returns to private capital is enough to
offset the triangle. Therefore we can ignore the B-S-B-S effect for
practical purposes. In short, then, the gain to native capital and
the loss to native labor almost wash each other out, and immigrants who
work in the private sector have little effect on native per capita income.

But we must still deal with the public sector, and to do that we
must estimate the returns to public capital, by analogy with private
capital. Let us make the simplifying asstimption that the capital/labor
ratio is the same in government as in industry. And for reasons of
data availability let us estimate the ratios we need from the non-
financial sector and project them to the entire private sector. Let

W = the amount paid for their labor to employees in
wages and salaries in industry, $1387 million in
1979

R = returns received after corporate taxes by owners for
P the use of their capital, $390 million

Q = total of employee compensation and after-corporate-tax

^ returns to capital = W + R = $1777
R P P

■jr^- = proportion of total returns that go to capital = 22%

P
On standard classical assumptions we may identify the share received

by labor as labor's marginal product. That is, the marginal immigrant

-7-

i

receives (100% - 22% =) 78% of the total additional product due to
him or her, and the owners of the capital receive 22%. We could also
use the stylized 25%-75% split used by Usher without changing our
result. And to repeat a point made earlier, if natives own the capital,
then the gain to native capital owners balances out the loss to native
workers. But if there are no returns to native capital owners, and
the immigrant receives the returns to both his/her labor and to the
capital he/she works with — as is the case in the public sector — there
is a loss to natives due to the capital-dilution effect, which makes
the marginal product of labor lower than otherwise. If we assume a
Cobb-Douglas production function and the quantity of capital temporarily
fixed, returns to native workers would fall by an amount roughly equal
to the amount implied by the 22% gain to capital owners.*

To allow for the immigrants working in the public sector, we must
obviously know the proportion working in the public sector. From the
cohort of persons who arrived between 1965 and 1970, there were in 1970
38,427 males and 24,256 females, out of 454,872 and 309,090 total persons
in the cohort employed of age 16 or over, who worked for the government —
that is, 8.22%, which is much lower than the 16.5% among natives (U.S.
Bureau of the Census, United States Summary, Table 93). For those who
arrived 1960-64, 1955-1959 and 1950-1954, the percentages are 6.8%,
7.8%, and 9.0% respectively. Say an average of 8% for all immigrants.
(Immigrants arriving more than twenty years earlier are not very
relevant to a policy analysis.)

♦Distributional effects are not considered here. In thinking about
that topic, it is important to keep in mind that the "worker" class actually
obtains much of the returns to capital through capital ox^mership by pen-
sion funds.

-8-

If we now assume that the returns to the capital with which the
government worker cooperates come to the workers, and assume also the
same capital/labor ratio and average salary as in industry, then 8%
of the total returns to private plus public capital due to immigrant
production flow to the immigrant. This is a far cry from the 58%
figure that emerged from Usher's method applied to the U.K.

A more meaningful comparison is the total amount that natives'
incomes fall relative to the total wages of immigrants (or relative
to the total additional product caused by the immigration). The
effect on native's incomes may be calculated as

Effect on natives = Income of natives afterwards minus income of

natives before the immigration = total output
after minus total output before minus amount
going to immigrants in wages and capital capture

= (Q+AQ) - Q - [ALCw+Aw)] - 4)[K(r+Ar)]

= AQ - ALCw+Aw) - ())[k(r+AR)

= ALCw+Aw) + AK(r+Ar) - AL(w+Aw) - (j)[RCr+Ar)]
where <J) is the proportion of the returns to
capital captured by the immigrants.

And because AK = 0 we can simplify

Effect on natives = <})[K(r+Ar)]

which is the total amount of the returns to capital that is captured by
immigrants. In Usher's calculation (fi = .58, whereas in our calculation
9 = .08*. The ratio of the effect on natives to the total wages of

immigrants, then, is "P^^)^^^^^ \ With Usher's <i> this ratio is about

*Usher's calculation is for the U.K., whereas ours is for the U.S.,
but that difference is a minor matter in this context.

-9-

.199, whereas with our <J) the ratio is about .028 using Usher's 75% share
to labor, or .025 using the above-calculated 78% share to labor.

The difference in implications between Usher's figure and ours is
major no matter how you look at it, whether from an average native's
point of view, an average native worker's point of view, or anyone else's
pocketbook point of view. And a major policy implication of this dif-
ference appears in a more global analysis of the effects of immigrants.
In the U.S. the balance of taxes and welfare expenditures is such that
natives gain considerably from the presence of the average immigrant
family, on a present value basis. On Usher's calculation, the loss to
natives on the production-and-income side would more than off-balance
the tax-and-welfare gain. Using our calculation this is not so; the
average family's net contribution to the public coffers far outweighs
the loss to natives through immigrant's capture of the returns to
capital,

CALCULATION OF THE BURDEN
OF DEMOGRAPHIC CAPITAL WIDENING DUE TO IMMIGRANTS

Above we discussed the dilution of public and private "production"

capital as it affects the earnings of natives. We must now also consider

public capital that immediately yields consumption benefits to natives

and immigrants, and whose use is subject to congestion. This includes

such "demographic capital" as schools and hospitals; more immigrants

imply that more of such capital is needed if service standards are not

to fall. On the other hand, the Statue of Liberty, intercity highways,

and space exploration installations pretty clearly are public goods

whose use by natives is unaffected by the number of immigrants. Some

-10-

capital, such as new highway construction around cities, and new physics
laboratories at universities, is difficult to classify, but luckily most
public capital falls pretty clearly into one or another of these two
categories.

A simple yet satisfactory rule of thumb* is that most chunks of
federal capital are true public goods, while most chunks of local and
state capital are demographic and subject to congestion. The state-
and-local category corresponds fairly closely to the categories of edu-
cation and hospitals and local roads. It would probably be possible to
work with the latter functional categories rather than with the federal
versus state-and-local distinction, but the results would not likely be
substantially different.

It may help to begin with this question: Why does any community
allow additional native American persons to move into the tax district
without assessing penalties to pay for the public capital the person
will use? A church or synagogue or mosque that builds a new building
free and clear from savings or current assessments is likely, for a
number of years after the new building is built, to assess a new member
a special building fee over and above the dues that old and new members
pay. Why does not a city or state do the same (assuming away legal
impediments)? The answer would seem to be that new members of a
community pay on average "rent" for the capital they use, at least
enough to cover a considerable part of the additional cost of
any necessary capital widening on this account. This is because — in

*Fred Giertz suggested this.

-11-

contradistinction to a religious congregation that finances a new
building without borrowing — a large part of public capital is built with
borrowed money. And with their taxes, new dwellers help pay the service
of this debt to an extent that the new dweller is not a burden on old
dwellers in this respect.

If all demographic construction — such as schools and hospitals and other
local facilities whose size must be affected by numbers of people (called
just "construction" or "structure" hereafter) — were financed by consol
bonds, the immigrants would be paying more taxes than if they used only
structures built for them and if they also paid entirely for that con-
struction which they used. (Underlying the latter part of this sentence
is a model of constant iiranigration under simple conditions. For now this
is only to be a vague statement of self-financing as the benchmark.) This
is simply because immigrants and their descendants would then be paying
a full share for all new construction, and would be paying also for some
structures that had obsolesced and were no longer in use; by the same
token, they would be paying more than their share for partly-obsolesced
structures .

On the other hand, if all construction were paid for on a current
basis, immigrants would underpay for the structures they use, because they
would pay only a part (on a per head basis equal to natives) for the new
construction necessary for them, whereas all of the cost of the new
construction would be due only to them (causing increased expenditure
by natives for the new construction) while not paying at all for existing
structures they would be using. And if the number of immigrants were small
and there were little or no physical depreciation, natives would pay almost

-12-

the entire cost of structures for immigrants. This point comes out
clearly if we notice that if all construction depreciated in say a year
(the tax period), natives would not be footing any of the bill for immi-
grants; all would then be on an equal footing. But since depreciation
takes longer than the current period, and since natives have already built
and paid for much of the construction they need, the additional construc-
tion for natives would be more than they would otherwise need (by a pro-
portion greater than the proportion of new immigrants to natives). This
last statement has not been stated rigorously, but should be made con-
vincing by this third possibility: With respect to construction financed
by debt, if the length of life of construction equals the length of time
during which the debt is serviced, asssuming equal payments on the debt
each year (that is, assuming that the building collapses the day it is
paid off), and if the cost of construction and quality of buildings re-
main constant, then an immigrant would exactly pay for the cost of new
construction built on his or her account. He/she would a) pay a full
share for new buildings built this year, like any native; b) pay nothing
for buildings no longer in use; and c) pay proportional to the remaining
length of life for older buildings still in service.

Therefore, we wish to combine the necessary elements — length of
capital life, length of bond period, proportion of capital financed by
borrowing, together with the cost of equipping an average immigrant
family — into an estimating equation, develop estimates of the elements,
and calculate the burden on immigrants per immigrant family. We begin
with notation:

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Cost of contruction per unit
of capital necessary for

an additional family = C

Proportion of construction cost

financed by bonds = c

Length of life of a unit -I

Bond period = b

Total native population of families = P = P

t t-1

Units in existence • . = Q» and Q/P = 1

Units built = q

Number of immigrant families = 1=1

Expenditures = E

Taxes, total paid = T

Without immigrant superscript = o

With immigrant superscript = I

Q = P
t t

q° = -4 Q^_n in steady state, the number of units necessary
to replace units worn out after H years,

1) ^t ~ T '^t-l ^ expenditures each year in steady state

without the immigrants

2) ^t ~ T ^t-1 ^ ■*■ ^ expenditures with the immigrants, because

one additional unit is needed for I

^^ ^t° = i ^^t-b ^ i -^Cb+i '"^''h^ ^^-^K = ^t ^^ '^^^^y

state, that is, total taxes yearly without immigrants, which includes

-14-

debt payments on capital financed in the past plus current payments
on the portion of current expenditures not financed by debt*

T° - Q° C

— = r = yC because Q = P^ = P. , , taxes per person

^t ^t ^ t t-1

without "immigrant in steady state

4) T = E + — cC + (l-c)C because the firsfr payment on the
financial portion of additional unit will be made in t, plus the non-
financial portion's payment

5) T^ - T^ = T- cC + (l-c)C increase in total taxes in t due

t to

to immigrant

1 T^ c 1

6) -g cC + Cl-c)C - pVT Cr + 1-c - y)C is the increase in burden of
taxes to natives in first year because of an immigrant. The total

burden over the years to natives is

7) b(— - y)cC + (l-c)C because of the payment on the finance
portion of the increment until the additional unit is paid for. Aside from
that, immigrant henceforth simply constitutes a proportional increase in the
society and has no effect on natives.

*We shall assume that the bonds are amortized at a constant rate
over their lives, that is, equal payments in each period until retire-
ment, in the manner of a house mortgage. In reality, a given bond issue
is floated with bonds of a variety of maturities, and the tax burden
declines as more bonds are retired. But the constant-amortization
assumption must be a satisfactory approximation for our purposes here.

-15-

8) The overall magnitude of the loss to natives (if there is one)
depends, of course, upon the proportion of capital investment that is
funded with debt, and upon the cost of the units, but also heavily upon
£, the length of life of the structure. If I is very short, the
immigrants pay for structures already destroyed, even if the bond period
is also short. If the length of life is very long, then the cost to
natives approaches the full cost of the structure. Therefore, to estimate
the effect, we need to know C, b, H. I/P may be assiamed to be very
small.

9) We may estimate C in several rough ways which, if they generally
agree, should allow us to have some confidence in the composite estimate.
(1) The current replacement value of government capital (structures,
inventory and equipment) at the end of 1975 was estimated by Kendrick
(1976) to be $981 billion. Dividing that total among units of govern-
ment on the basis of capital outlay figures by the various units of
government plus tentative depreciation yields an estimated $781.5 bil-
lion as the value of state and local capital at the end of 1975. Its
ratio to GNP in the corresponding year was 38.1 percent. Therefore,

one may assume that it costs an amount equal to that proportion times
the representative family's income to equip an additional representative
family.

A rough check for this magnitude uses the observation that employment
in the state-and-local sector is 14.1 percent of all employment. If the
capital-output ratio is 2 in that sector as in the rest of the economy,
and if average income is the same in that sector as is the rest of the
economy, then a sum equal to 2 x 14.1% = 28.2% average income is the value

-16-

of such capital for the average family. The value in 1979 for the median
primary family (Statistical Abstract of the U.S., 1980, p. 451; the mean
value for all families would be better, but will not be sufficiently dif-
ferent to make a difference here) was (.381 x $19,684 =) $7500.

10) The average bond period b is 10.53 years, estimated as described
in the appendix.

11) The average length of life of state-and-local capital is
14.76 years, estimated as described in the appendix.

12) The value of c, the proportion of the capital that is financed
with debt, is approximated .62, as described in the appendix.

13) Calculating now by inserting the necessary values into (7) the
average cost to natives of equipping an immigrant family, assuming the
family's income and use of services is average, is then $4172 or 21%

of a year's income for a family, without discounting the future pajrments.

Without further ado or the relatively minor adjustments called for
by a variety of factors working in both directions, let us hit upon one
fifth of the average family's inocme as the cost of equipping the
community for an additional average family's needs. For this to be an
appropriate cost for an average immigrant family requires that it be of
the same size and composition as an average native family. This is
probably not so far from the fact as to make inappropriate 21% of family
income as the estimate.

This cost is certainly not negligible even when the returns to gov-
ernment capital from government immigrant workers are added. However,
it is considerably smaller than the present value of the net of taxes

-17-

paid and transfers received by immigrants — which are perhaps 1.5 or 2
times the average native family income (Simon, 1981) — and hence the
capital effect does not dominate the overall impact of immigrants upon
natives' standard of living, which is positive on balance even without
considering the effect on natives through increased productivity, and
the latter almost surely swamps all other effects in the long run (Simon,
1982).

SUMMARY AND CONCLUSIONS

There are three questions about capital and immigrants we must
answer: The effect through private capital which immigrants work with,
the effect through public capital that immigrant workers use, and the
effect through public capital used for services by immigrants.

The first question, the issue of private capital dilution, can be
dealt with swiftly. Sorts and Stein, and Berry and Soligo, showed that
while workers as workers lose through lower wages due to immigrant
workers, owners of capital benefit by something more than the workers
lose, and hence per-person income goes up in the society. The overall
effect is small by Usher's and Simon's reckonings, perhaps 1% or 2%,
small enough to forget.

If all immigrants worked in private industry, and if there were no
corporate income taxes, we could now also forget about the entire sub-
ject of production capital dilution. Usher tackled the second and third
of these problems together by analyzing the properties of public and
private capital for the U.K. Simon did much the same for Israel, inde-
pendently. Usher arrived at the conclusion that 58% of the returns to
all the capital they work with are captured by immigrants even if they

-18-

own no private capital, and therefore immigrants are a major burden
upon natives. And of course in Usher's model there is no positive
effect of immigrants upon productivity to counterbalance the effect
Usher calculated. For the productive capital, we estimate that immi-
grants capture the returns from only 8% of the capital they work, with,
which is the government capital only; the result is a loss of perhaps
2% of an immigrant family's income for one year, which is about the same
size as the gain to natives through the private capital that immigrants
work. with.

The cost to natives of equipping the immigrant family with "demo-
graphic capital" — schools, hospitals, and local roads — depends upon the
cost of such equipment, the proportion financed by bonds, the average
length of life of the capital, and the average bond life. We develop
an estimating equation, and calculate that the cost to natives in 1975
dollars is $4172, about a fifth of a year's income of an average family.
This is not insignificant in magnitude, but this amount — together with
the effect through productive capital dilution discussed in the first
part of the paper — is considerably smaller than the benefits of immi-
grants to natives through their relatively low use of welfare services
and their relatively high contribution of taxes.

-19-

References

R. Albert Berry and Ronald Soligo, "Some Welfare Aspects of International
Migration," Journal of Political Economy. 77:778-94, Sept. /Oct. 1969.

George H. Borts and Jerome L. Stein, Economic Growth in a Free Market

(New York: Columbia University Press, 1966). Quoted by Usher, 1977.

John W. Kendrick, et. al.. The National Wealth of the United States
(New York: The Conference Board, March 1976).

Julian L. Simon, "The Economic Effect of Russian Immigrants Upon the

Veteran Israeli Population: A Cost-Benefit Analysis," The Economic
Quarterly, 23, August 1976, pp. 244-253, (in Hebrew).

Julian L. Simon, "The Really Important Effects of Immigrants Upon Natives'
Incomes," in Barry Chiswick (ed.). Conference on Immigration,
(Washington: American Enterprise Institute, forthcoming).

Julian L. Simon, "What Do Immigrants Take From, and Give to, the Public
Coffers?" done for the Selection Commission on Immigration and
Refugee Policy, August, 1980, to be published in Spring, 1981.

Dan Usher, "Public Property and the Effects of Migration Upon Other

Residents of the Migrants' Countries of Origin and Destination,"
Journal of Political Economy, Volume 85, 1977, pp. 1001-1026.

M/D/329

APPENDIX

Estimating the Length of Life of Capital
1') K = Cq + (l-d)C + (l-d)^C2 + ... Adam and Eve

where !

K = current value of total demographic capital
c. = construction cost of demographic capital i periods ago
d = rate of depreciation.
Now, let:

2') C. =C.^^(l+g)

where :

3') g = d + p + r + s

Here we argue that the rate of growth of construction is equal to the
rate of depreciation plus the population growth rate (p) plus the rate
of inflation (r) plus the rate of increase of the standard of unit pro-
vision (s).

Inserting 2' and 3' into 1' and solving the infinite series yields:

n 1 A

4') K = lim E [.^ ill. ^AC.

_ "• 1+r+p+s+d ■" 1
n^« 0 '^

^ ,l+2(rj2+s)+3d,
0 ^ r+p+s+d J

Solving;

l+(2 - ^)(p+r+s)
5') d^ ^

^- 3

-A2-

Finally:

6') ^4

Here we estimate the values of i and d by using national wealth
estimates from Kendrick, et. al. (1976), population growth data from
the Bureau of the Census, and price data from the Bureau of Labor
Statistics,, and income data from the Department of Commerce. Kendrick
estimates that the value of government wealth in structures, inventories,
and equipment was $815 billion in 1973, valued in current dollars.
Gross investment in 1973 was estimated to be $85.5 billion.* Since
Kendrick does not provide separate estimates of state and local wealth,
we assume the average depreciation rate to be the same in all government
sectors.

From 1960-73, the U.S. population grew (p) at an estimated annual
rate of 1.19 percent. The average price of government purchases (r)
increased at a rate of 4.73 percent. We use as a proxy for the increase
in the standard of public good provision (s) the increase in real per-
capita gross national product from 1960 to 1973, estimated to be 1.49
percent.

Inserting these estimates into formulae 5' and 6' yields
d = 6.78 percent
a = 14.76 years.

*These estimates were derived by continuing the relationship re-
vealed in Tables 2-1 and 3-A in Kendrick (1976).

-A3-

Estimating the Bond Period
Let:

1") D = I - R + I - R + . . . Adam and Eve

where :

D. = current value of debt end of period i

I. = gross borrowing i periods ago

R. = debt retirement i periods ago.

This says that the current value of the debt is equal to the sum of all
past borrowing minus debt retirements. It follows that:

2") I. = D. - D. , + R.
11 1-1 1

This says that gross borrowing in period i equals the value of ending
debt minus beginning debt plus bond retirement during period i.

If we assume a maturity period equal to b — the value to be esti-
mated— we get :

3") R. = I. + b
1 1

recalling that b = bond period.

That is, debt retirement in period i equals gross borrowing b periods

previous. Then, it follows that:

4") D- = lim E I. - lim Z I.
n-*<» 0 n^«> b

= lim [Z I. - E I.]

n-^ 0 ^ b ^

To facilitate the solution we assume;

-A4-

5") I. = I._j_^(l+g), where

g = the rate of growth of borrowing

Then:

^0 y^

and, finally:
7") b =

ln(-^) - InClQ + -^ - Dq)
ln(l+g)

Using the above formulae we estimate the average maturity of
debt (b) based on data for the period 1960-73. Census of government
data show state and local net debt of $158.7 billion in 1973, new issues
of $21.8 billion in fiscal 1973, and a grand rate of 8.07 percent in
new issues over the is period. Plugging these figures into formula 7"
yields :

b = 10.53 years. ' ^

Financing Capital Outlay
Next we estimate the percentage of capital outlay that is financed
by bond issuance. We assume that all debt retirement is tax financed
as part of the normal amortization process. It follows that proceeds
of all long-term debt issues are used to finance capital outlay. We
use figures from 1973 for purposes of comparability with data we used
to estimate other parameters in our argument.* Thus:

*Data are taken from U.S. Bureau of the Census, Compendium of
Government Finances, 1972-73.

-A5-

p _ new bonds issued _ $21.8 billion _
capital outlay $35.3 billion ~

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CKMAN m
)ERY INC. |M1

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o-Pkuf N. MANCHESTER.