Effect of Unemployment Insurance Tax On Wages and Employment: A Partial Equilibrium Analysis

Effect of Unemployment Insurance Tax On Wages and
Employment: A Partial Equilibrium Analysis

Deergha Raj Adhikari, Oklahoma Employment Security Commission
Lynn Gray, Oklahoma Employment Security Commission
Jackie Burns, Texas A & M University

JEL Classification: J31
Key Words: unemployment insurance tax, wage, employment
Abstract
We develop a partial equilibrium model under a cost minimization problem to derive the
effect of an unemployment insurance tax on average wage rates and employment. We
assume perfect competition in the product market and perfect factor mobility in the factor
market. Our model suggests that a portion of the tax is passed on to employees by means
of reduced wages. The model also suggests that a lower level of employment will be
realized as a result of the tax.

Deergha Raj Adhikari
2401 N. Lincoln Boulevard
Oklahoma City, OK 73152
Phone: (405) 962-7587
Fax: (405) 525-0139
E-mail: deergha.adhikari@oesc.state.ok.us








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Effect of Unemployment Insurance Tax On Wages and
Employment: A Partial Equilibrium Analysis


Abstract
We develop a partial equilibrium model under a cost minimization problem to derive the
effect of an unemployment insurance tax on average wage rates. The model suggests that
a portion of the tax is passed on to employees by means of reduced wages.

1.
Introduction

The unemployment insurance (UI) tax is a federal tax collected by the U.S.
government from employers across the country. Most of the tax revenues is then
transferred to the related states in terms of Unemployment Insurance Trust Funds. This
fund is then used by the states to pay compensation to unemployed workers actively
seeking jobs. The UI tax is “experience rated,” which means each employer does not pay
the same tax amount for each of its employees. In the product market, however, each
employer faces more or less the same price line. This situation gives rise to the belief that
employers must have incentive to shift such taxes in order to stay in the market. With
diminishing return in production, a downward shift could take place in terms of 1) a
lower payment to the worker, 2) a reduction in the employment, or 3) a lower payment to
the factor whose supply is less elastic. From a policy perspective, analyzing the ultimate
incidence of an unemployment insurance payroll tax and its effect on wages and
employment is very useful.

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In the past, there have been a few works done on the incidence of UI tax. In his
seminal paper, Lester (1962) assumed a competitive equilibrium in both product and
factor markets and concluded that the firms themselves bear most of the incidence of a UI
tax. Hamermesh (1977) takes this issue to the long run and concludes that the consumers
and the workers of a firm share the incidence almost equally. Patricia and Meyer (1997),
using data from eight states for the years from 1978 to 1984, analyzed the effect of UI tax
on wages and employment. They concluded that individual firms are only able to pass on
a small portion of UI tax that, in turn, lead to substantial employment reallocation across
firms. They also conclude that experience-rated taxes can be used to reduce a temporary
layoff, as the differences in taxes are not easily shifted to workers.

The works done so far on the incidence of UI tax have mostly derived their results
from a labor market equilibrium condition. These studies implicitly assume a cost
minimizing behavior on the part of the firms. Our paper will explicitly analyze the cost
minimizing behavior of the firms in a competitive market and show how a change in UI
tax affects the equilibrium wages and employment. Section 2 presents a theoretical model
and derives the results. Section 3 concludes the theoretical results.
2.
The Model
We assume that the typical firm only employs two factors and produces a single
good with a technology represented by the Cobb-Douglas production function as follows:
? ?
Y = AK L ,








(1)
where A is a constant factor, K and L are amounts of capital and labor respectively, and ?
and ? are coefficients of capital and labor respectively. The cost function of the firm is
assumed to be linear as follows:

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C = PLL + IK,








(2)
where C is the total cost, PL is the tax-included wage rate, and I is the interest rate facing
the firm. Suppose the firm pays unemployment insurance tax to the federal government,
which is collected per unit of labor at the rate of T. Therefore, the tax-included wage rate
can be expressed as follows:
PL = W + T,








(2a)
where W is the wage rate. The cost-minimization problem for the firm, given the output
constraint and characterized by the Cobb-Douglas production function, can be shown as
follows:
?
? ?
= PLL + IK + ?(Y - AK L )




(3)
First Order Conditions:
?
?
?
? 1
=
?
?
??
= 0






(4)
?
P
A K L
L
L
?
?
? 1
=
?
I ?
?
A
??
= 0






(5)
?
K L
K
?
? =
?
?
Y ? A
= 0







(6)
?
K L
?
Taking the ratio of equation (4) and (5) yields
?K
PL =

I
L
?
Solving for L yields
I
?
L =
.
K
.









(7)
P ?
L
Substituting equation (7) into (6) yields

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---

I ?
?
?
Y - A
(
. .K) = 0
K

P ?
L
Solving the above equation for K yields
1
?
?
Y +
I ?
?
?
? + ?
K = (
)
(
. )







(8)
A
PL ?
Substituting the value of K into equation (6) yields
?
1
??
?
?
Y ?+?
I ? ?+?
?
?( ) ( . ) ?
Y - A
L
?
= 0
A
P ?
?
L
?
?
???
? +
??
?
I
?
?
?
?
Y –
. ?+? ?+
A A
? (
. )
= 0
Y
L

P ?
L
?
Solving for L yields
?
?
?
?
I ? ??
? + ?
?
1
L = Y
? + ?
? + ? (
. )
A A Y

PL ?
Solving for L yields
1
?
L =
? + ?
Y
I
? ? + ?





(9)
(
)
(
.
)
A
P L ?
Substituting equation (8) and (9) into (2) yields
1
1
??
?
Y +
I ? ?
?
? +?
? + ?
Y
I ? ?+?
C = P ( )
(
. )
+ I (
)
(
. )

L
A
P
A
PL ?
L ?

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---

?
?
?? ?
? + ?
? + ?
1
?1
?
?
? ?
?
?
= Y ?+? A?+? P ?+? ?+ ( )
+

L
I ? ?
( )
?
? ?
?
?
?
?
Denoting ?+? by r, the above equation can be rewritten as
1
?1
?
? ? ?
??
??
?
C = Y r A r P r
?
?
r
+
?
? r
r
? r
L
I r ?
?
?
?
[
1
?
?
1
?
? ?
A? ? ]
= r
r Y r I P r
r

L
[
1
?
??
A
? ?]
Denoting
r by s, the above expression can be rewritten as
?
1
?
C = s.Y r I P r
r

L
Suppose, the firm’s revenue function is Cobb-Douglas type as follows:
?
?
R = B P
,
L I
where B is a constant, P is the price of labor, and I is the price of capital. We assume
L
that there is perfect competition, so that the firm makes no economic profit, and its total
revenue ( R ) is equal to its total cost ( C ). As such, we have the following equilibrium
condition:
?
1
?
?
?
B P
= s.
r
r
r

L I
Y I PL
Rearranging the terms in the above equation yields
? ??
s
1
? ?
?
P r =

L
Y r I r
B
Solving the above equation for PL yields

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r
s ?? ??
1
? ???
P =
?? ??
?? ??
( )

L
Y
I
?
Since PL = W + T as shown earlier, decomposing it yields
r
s ?? ??
1
? ???
W + T = (
)
Y ?? ?? I ?? ??
?






(10)
Suppose the unemployment insurance tax is a constant function of the wage rate such that
T = tW. Then, equation (10) can be rewritten as
r
s ?? ??
1
? ???
W + tW = (
)
Y ?? ?? I ?? ??
?

Rearranging the terms in the above equation yields
r
?? ??
1
s
1
? ???
W =
( )
Y ?? ?? I ?? ??
1 + t
?
r
s ?? ??
1
? ??
?
1
= 1
( + ?
t) ( )
Y ?? ?? I ?? ??
?






(11)
Taking log of both sides yields
r
?
?
? s ?? +? ?
1
? ? ??
LnW = ln (
?
)
? ? 1
ln( + t) + (
) lnY + (
) ln I
?? ? ?
?? ? ?
? ?
?
?
?
?
?
= ? ? ? ln D + ? lnY + ? ln I




(12)
0
1
2
3

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---

?
r
?
?
?? + ?
s
?
1
? ? ??
where ? = ln?(
)
? , ? = 1, D = 1 + t, ? = (
) , and ? = (
) .
0
? ?
?
1
2
?? ? ?
3
?? ? ?
?
?
?
?
T
Since D = 1+ t = 1 +
by assumption, estimating equation (12) with restriction that
W
?1 =1 and testing if ?1 is negative will show if unemployment insurance tax (t) negatively
affects the wage rate. In other words, a negative ?1 indicates that the employer is able to
shift at least some of the burden of unemployment insurance tax to the employee by
offering reduced wages.
Effect of Unemployment Insurance Tax on Wages
Differentiating equation (11) with respect to t yields
r
?? + ?
dW
?2
S
1
? ???
= ? +
1
(
t) ( )
Y ?? +? I ?? ??
dt
B
dW
Since t, S, B, Y, and I are all positive,
< 0. This implies that an increase in tax rate
dt
causes the wage rate to decrease. The result suggests that the employer passes a part of
the unemployment insurance tax on to the employees by offering reduced wages. With
other factors remaining the same, this implies that the equilibrium levels of wages
decrease with the increase in unemployment insurance tax.


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Effect of Unemployment Insurance Tax on Employment
The equilibrium level of labor demand is given by the equation (9), which can be
rewritten as
1
?
Y +
I
? ?
?
? + ?
L = (
)
(
. )
,
A
W +tW ?
where price of labor, PL, is equal to the average wage rate, W, and the unemployment
insurance tax, T, which is tth fraction of the wage rate. The above equation can be
rearranged as follows:
1
?
Y ?+? I
? + ?
??
?
L = (
)
(
)
1
( +t)?+?





(13)
A
W?
Differentiating equation (13) with respect to t yields
1
?
? + ?
? + ?
?2? ??
dL
?
Y
I?
= ?
( )
(
)
1
( +t) ?+?
dt
? + ? A
W?
dL
Since Y, A, I, W, ?, ?, and t are all positive,
< 0. This means that an increase in the
dt
tax rate reduces the equilibrium level of labor demand. With other factors remaining the
same, this implies that the whole labor demand curve shifts downward following the
introduction of the tax. Therefore, the equilibrium level of employment decreases with
the increase in unemployment insurance tax.

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3.
Conclusion

Our paper theoretically examines the incidence of unemployment insurance (UI)
tax on equilibrium levels of wages and employment. Past researches on the incidence of
UI tax are mainly based on labor market equilibrium condition and implicitly assume a
cost minimizing behavior on the part of the firms. In our paper, we explicitly analyze the
cost minimizing behavior of the firms in a competitive market and show how a change in
UI taxes affects the equilibrium wages and employment. Our results suggest that the UI
tax negatively affects the equilibrium levels of wages and employment.
References
Anderson, Patricia M. and Bruce D. Meyer (August 1995). “The Incidence of a Firm-
Varying Payroll Tax: The Case of Unemployment Insurance,” NBER Working
Paper No. W5201.

Anderson, Patricia M. and Bruce D. Meyer (Dec. 1995). “The Effect of Unemployment
Insurance Taxes and Benefits on Layoffs Using Firm and Individual Data,”
NBER Working Paper No. W4960.

Anderson, Patricia M. and Bruce D. Meyer (1997). “The Effects of Firm Specific Taxes
And Government Mandates with an Application to the U.S. Unemployment
Insurance Program,” Journal of Public Economics, v. 65, PP. 119-145.

Hamermesh, D.S. (1977). “Jobless Pay and the Economy,” Johns Hopkins University
Press, Baltimore.

Kramarz, Francis and Thomas Philippon (Oct. 2001). “The Impact of Differential
Payroll Tax Subsidies on Minimum Wage Employment,” Journal of Public
Economics, v, 82, no. 1, pp. 115-146.

Kolm, Ann-Sofie (Nov. 1998). “Differentiated Payroll Taxes, Unemployment, and
Welfare,” Journal of Public Economics, v., 70, no. 2, pp. 255-271.

Lester R.A. (1962). “The Economics of Unemployment Compensation,” Industrial
Relations Section, Princeton University, Princeton, NJ


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