1

Productivity, Returns to Scale and Product Differentiation in the
Retail Trade Industry ∗--- An Empirical Analysis using Japanese Firm-Level Data --Atsuyuki KATO †Research Institute of Economy, Trade and Industry
Abstract
This paper examines productivity and returns to scale under the assumption ofmonopolistic competition using Japanese firm-level data. Although differentiatingproducts (services) is considered important in firms’ strategies and productivity growth,
it has not been sufficiently investigated in previous studies. In this paper, we study thisissue in two retail trade industries, department stores and supermarkets, applying themodel of Melitz (2000). Our results indicate that the retail trade industries possibly
follow increasing returns to scale if we consider the effects of product differentiation. In
addition, product differentiation has a positive effect on firms’ revenue. Thus, policy
measures that promote economies of scale and product differentiation should contributeto further growth in these industries. In addition, the results indicate that the regulatory
reform of the retail trade industry in 2000made a positive contribution.

∗

This research is a part of the project “Service differentiation and Productivity”
undertaken at the Research Institute of Economy, Trade and Industry (RIETI). The
author would like to thank Sadao Nagaoka, Masahisa Fujita and other seminar
participants at RIETI. The author also wishes to thank Hajime Takatsuka for his
helpful comments on the model. The opinions expressed and aurgments employed inthis paper are the sole responsibility of the author and do not necessarily reflect those of
RIETI.
†E-mail: kato-atsuyuki@rieti.go.jp

2“Productivity isn’t everything, but in the long run it is almost everything”--- Paul Krugman 1 ---1. Introduction
Productivity has been studied by economists and policy makers for a long time. This isbecause only productivity growth is considered as an engine to yield economic growthin the long run. The surge of productivity growth in the U.S. in the later half of the
1990s reinforces their interests. It shows that the service sectors which were thought asstagnant sectors before can also raise their productivity growth and become a driving
force of macro economic growth. To better understand these facts and obtain usefulimplications, many theoretical and empirical studies have been conducted. In particular,
the increased availability of micro (firm or establishment level) data has produced many
empirical papers to estimate productivity and examine the relationships between
productivity and industrial policy (including the regulatory reform).
In those studies using firm level data, differentiation of products (services) has notbeen well examined although it is thought to play some important roles in firm
strategies and productivity growth. This is partly because the data availability for
product differentiation is still poor, particularly for service producing firms. Neglecting
this problem in estimation, however, may bias the estimated returns to scale andproductivity. For this issue, Melitz (2000) proposes an interesting model which
incorporates monopolistic competition into the estimation of production function. His
model also explicitly tackles the problem that total sales are different from actual output
of firms’ production if product (service)-specific prices are heterogeneous although they

1 Krugman (1990)

3

are interpreted to be identical in estimating productivity. In this model, productivity
estimation does not rely on the product-specific price data although it imposes some
limitation on productivity estimation. Loecker (2007) modifies Melitz’s model adding
product-specific price data. This model improves estimation of productivity bydecomposing demand shocks and productivity growth. But, it is not much applicable forservice industries because service-specific price data are not usually available.
In this paper, we examine productivity, returns to scale, and product (service)differentiation, applying a slight modification of Melitz’s approach to Japanesefirm-level data. To the best of our knowledge, this is the first paper which incorporates
product differentiation into productivity estimation following Melitz. In addition, inorder to compare the results and discuss the effects of product differentiation on
productivity, we estimate three different models using data for the retail trade industry,in particular departmental stores and supermarkets. Furthermore, we examine therelationships between productivity and the regulatory reform.
The layout of this paper is as follows. In section 2, we detail the model which we
examine. Section 3 describes the data which we use. In section 4, we discuss theempirical results and their implications. And the last section draws concluding remarks
from the above discussion.

2. The Model
This section briefly describes the model which we examine. Following Melitz, we startwith the case where any firm produces a single product or service 2 . Suppose that firms
in an industry produce symmetrically differentiated products with a common elasticity
2 To avoid redundancy, the term, product, includes both meanings of product and service,henceforth.

4of substitution (CES) σ between any two of them. According to Blanchard andKiyotaki (1987), we assume the utility function of a representative consumer for
products in industry c is described as follows 3 :Uc = N

1
1−σ

σ −1
σ
i

⎛ N
⎜ ∑i =1 (Λ i Q )
⎝

⎞
⎟
⎠

σ
σ −1

,

(1)

where N is the number of firms in this industry 4 . Λ i and Qi denote the consumer’svaluation of the product quality of firm i , and the quantity of it, respectively. The
parameter σ is restricted to be greater than unity otherwise there might be noequilibrium. The utility function is assumed to be differentiable and quasi-concave. In
addition, an increase in the number of products does not change marginal utility after
1

optimisation because the utility function is normalised by N σ −1 . In this simple modelof monopolistic competition, changes in Λ i over time stem from changes in the actual
quality of the product or changes in the consumer’s preference. To simplify the model,
the shifts of preference which affect all products are excluded. For this utility function,
the budget constraint of the consumer to purchase products of industry c is

B = ∑i =1 Pi Qi
N

,

(2)

σ

σ −1
⎛ N
⎞ σ −13 Melitz assumes the utility function as⎜ ∑i =1 (Λ i Qi ) σ , Z ⎟ , where Z is an overall⎝⎠

demand shifter. But we don’t follow it because equation (1) is mathematicallycompatible with the following equations.
4 Holtz-Eakin and Lovely (1996) uses a similar framework of differentiation for
production function with a large input variety (in particular, intermediate inputs).

5

where Pi is the price of firm i ’s product. From the first order condition of utility
maximisation, we obtain the following:1−σ~ ⎛⎜ 1 N ⎛ Pi ⎞
⎜ ⎟
D ≡P=
⎜ N ∑i =1 ⎜⎝ Λ i ⎟⎠
⎝
−1

⎞
⎟
⎟
⎠

1
1−σ

,

(3)

~
where P is the average price of products adjusted on the quality in this industry 5 .

From the above equations, the demand for firm i ’s product is written as follows:− (1−σ )iQi = Λσ⎛ 1 ⎞ ⎛P⎞
⋅ U c ⋅ ⎜ ⎟ ⎜ ~i ⎟⎝N⎠ ⎝P⎠

−σ

,

(4)

Now, we denote the sales of firm i ’s product as Pi Qi = Ri , and total sales in theindustry which is equivalent to total revenue as ∑i =1 Ri = R . Using them, equation (4)Nis rewritten as follows.

σ −1

Qi = Λ i⎛ Pi ⎞
⎜ ~⎟
⎝P ⎠

−σ

1 ⎛R⎞
⎜ ~⎟
N ⎝P⎠

(5)

This equation indicates that the number of firms which equals the number of products
determines output of firm i , together with other factors.
On the other hand, the production function in this paper is defined as follows. First,
5

D is a Lagrange multiplier.

6

we assume that firms use the production technology which is homogeneous of degree

γ > 0 . We do not assume that γ = 1 but rather examine this issue empirically. Χ i isthe vector of inputs which are consumed in production of Qi . X i is an aggregate
input index which is constructed as a linearly homogeneous function of inputs, f (Χ i ) .
Similarly, the vector of the factor prices is Ω i , and an aggregate factor price index is
Wi = h(Ω i ) . Following them, our production function for firm i is described asfollows:

Qi = Φ i X iγ ,(6)where Φ i represents productivity of firm i .
Now, we take logs of equation (5) and (6), and solve the demand function forfirm-specific price p i . Plugging in the production and the inverse demand functions
into the revenue function, ri − ~p = qi + pi − ~p , we obtain the following revenue
production function:

1
σ −1
σ −1
(φit + λit ) ,rit − ~
pt =γxit + [(rt − ~pt ) − nt ] +

σ

σ

σ

(7)

where lower case variables are logs of upper case variables in equation (5) and (6). The
subscript t represents time. From the definition of Φ i and Λ i , φit + λit is a quality
adjusted productivity index, and is denoted as ϕ it = (φit + λit ) . Without additional
information, neither φ it nor λit is separately identified.
As Melitz details, equation (7) does not include the product-specific price which is7

not usually available in empirical study. Equation (7) also reveals that estimation ofrevenue production function without product differentiation may understate the degreeof returns to scale by

σ −1. This is consistent with a finding of Klette and Grilichesσ(1996). Productivity differences Δϕ it are also understated by

σ −1
as well. Inσpt ) does not always obtain aaddition, an industry aggregate sales regressor (rt − ~significant and positive coefficient, and only the estimated coefficient greater than 1 σ
possibly means that there are external economies unlike Cooper and Johri (1997) 6 .
Next, we expand the above model to the case where firms produce different
numbers of products. Now, firm i produces M i products. Since we do not add anychange on the structure of the model, the production and demand are respectively
presented as follows;

Qij = Φ ij X ijγ ,⎛ Pij ⎞
Qij = Λ ij ⎜⎜ ~ ⎟⎟
⎝P⎠
σ −1

(8)

−σ

1 ⎛R⎞
⎜ ⎟,
M ⎝P⎠

(9)

i
where M = ∑i =1 M i . We also assume ∑i =1 ∑ j =1 Rij = ∑i =1 Ri = R , Pij Qij = Rij and

N

N

M

N

X i = ∑ j =i1 X ij . We add the assumption that introducing an additional product has aMsunk cost for firms as well. An average quality adjusted productivity for each firm isdenoted as ϕ~i , and formulated as follows:

6 Melitz also discuss issues related to firm markups, and concludes that productivity

differences can be separately estimated without firm specific price information because
the firm markups is inseparably related to the inputs.

8

1
− ϕ~i

e γ

⎡
1
M i ⎢ ⎛ M i R ij ⎞=∑ j =1 ⎢ ⎜⎜ R ⎟⎟
Mi
i
⎠
⎢⎣ ⎝

σ
σ −1

⎤
−ϕ
e ij ⎥
⎥
⎥⎦

1

γ

,

(10)

where ϕ it is a quality adjusted productivity of each product. Under these assumptions,a revenue production function of firm i divided by the number of products at period t
is described as follows.

σ −1
σ −1 ~
1rit − mit − ~pt =γ (xit − mit )xit + [(rt − ~pt ) − mt ] +
ϕ it
σ

σ

σ

The term mit in the left hand side is transposed to the right hand side. Then, thefollowing revenue function of firm i is obtained.

σ −1
1
σ −1 ⎡~ ⎛ 1⎞ ⎤rit − ~
pt =γxit + [(rt − ~pt ) − mt ] +ϕ it + ⎜− (γ − 1)⎟mit ⎥
⎢
σ
σ
σ ⎣
⎠ ⎦
⎝ σ −1In this equation, as Melitz discusses, the term(11)

1
− (γ − 1) should be larger than zero
σ −1

if firms produce more than one product while the positive effects of increasing productvarieties for each firm have a trade-off against increasing the sunk cost.
Following Levinsohn and Petrin (2003) (henceforth, LP), we estimate equation(11). LP discusses the issue of potential correlation between inputs and productivity andproposes to use the intermediate input’s demand function which is assumed as amonotonic function of productivity 7 . Inverting the monotonic function can uncover the
7 Olley and Pakes (1995) also propose an approach where the estimation of production

9unobserved productivity term as a monotonic function of the intermediate input andcapital 8 . To discuss a bias in returns to scale and effects of product differentiation, we
examine the models with three different assumptions, (1) products are homogeneous
across firms, (2) the average number of products per firm is constant over time, and (3)the numbers of products vary across firms. For assumption 1, the estimated model isequivalent to the LP model. An equation based on assumption 2 is equivalent to themodel proposed by Melitz and is described as follows.

rit − ~
pt = β 0 + β k k it + β l lit + β e eit + β σ [(rt − ~pt ) − nt ] + ϕˆ (k it ,eit ) + u it

where ϕˆ (k it , eit ) =σ −1 ⎧⎡ 1⎤ ⎫− (γ − 1)⎥ mit ⎬ .
⎨ϕ it + ⎢σ ⎩⎣σ − 1⎦ ⎭(12)

On the other hand, the modelwith assumption 3 is a modified one of equation (12) and is written as follows.

(
rit − ~
pt = β 0 + β k k it + β l lit + β e eit + β σ [(rt − ~pt ) − mt ] + β m mi + ϕ (k it ,eit ) + u it

(13)

σ −1
(
where ϕ (k it , eit ) =ϕ it . An issue which we should discuss is what variable isσexamined as a proxy of the number of products sold by a firm. In this paper, we use thefloor space per shop for each firm under an assumption that firms with similar businessmodels in the retail trade industry follow similar use of space for their commercial
establishment 9 . Estimating these three equations, the LP equation, equation (12) andfunction suffers problems due to endogeneity. Unlike LP, they propose to use investment
as a proxy of unobserved productivity. It, however, has a significant shortcoming thatinvestment data contain many zeros in conventional firm level data. Dropping many
zeros remains the simultaneity problem unsolved.
8 Souza (2006) details the LP methodology under monopolistic competition.
9 This assumption seems to be reasonable between firms in the same country.

10(13), we examine productivity, returns to scale and product differentiation.

3. DataIn this study, we use firm-level data of the retail trade industry in Japan over the
1995-2004 period. In particular, we focus on firms categorised as the department storesand supermarkets. The data are extracted from the annually compiled official statistics
of firms’ activities by the Ministry of Economy, Trade and Industry of Japan 10 . This
statistics cover many activities of firms and are considered reliable11 . In addition, we
obtain figures on floor space of shops for each firm from the statistical yearbook named
as Nikkei Almanac of the Distribution Industry. To construct a proxy of firms’ productvariety, they are divided by the number of commercial establishments for each firm.
From these data source, we construct our own dataset composing of total revenue,
labour, capital and intermediate inputs, and floor space per shop for each firm.
In our dataset, total revenue of each firm is represented as total sales. The proxy ofaccumulated capital is the tangible fixed assets. Labour input is calculated as
man-hours 12 . Following Tokui, Inui and Kim (2007) and Kim, Kwon and Fukao (2007),
henceforth KKF, the intermediate input is obtained as follows 13 :Intermediate Input = COGS + SGA − (TW + Dep + T & D + Purchase) , (14)where COGS, SGA, TW, Dep and T&D are the cost of goods sold, the selling and
10 This statistics is named as ‘the Basic Survey of Business Structure and Activity’.
11 Kiyota and Matsuura (2004)

12 The data of working hours are available from Monthly Labour Survey.

13 In calculation of intermediate input, we slightly modify both Tokui et al. and KKF.

The former does neither include tax and dues nor purchase in calculation of theintermediate inputs while the later does not include tax and dues.

11general administrative expenses, the total wages, the depreciation and the tax and dues,
respectively. In constructing our dataset, we rule out the firms which report zero or
negative values as total sales, the number of regular workers, the tangible fixed assets,
total wage, or intermediate inputs. Since figures on total revenue, capital andintermediate inputs in the original data source are reported as nominal values, we needto construct real series of those variables using reliable deflators. For total sales andintermediate inputs, JIP industry-specific deflators of output and intermediate input areused 14 . Capital is reported as book values including the land possessed by firms in thedata source. We construct real series of capital following KKF. However, we don’t
subtract the estimated values of the land from the values of the tangible fixed assets
because we consider the land is an important factor for production, particularly in retailtrade industries.

4. Empirical Results
This section discusses the results of estimation and their implications. But, before that,
we should discuss an issue related to the deflators. In our model framework, theindustry-specific price index is defined as an average price of products adjusted on their
quality. The actually available price index is, however, not exactly identical to that one.
It means that our estimation might obtain biased coefficients. In fact, this is a
shortcoming not only in our estimation, but also in all empirics using time series data 15 .
But we do not think that it significantly harms our empirical analysis. Since equation (3)is essentially the methodology used to construct the industry-specific price indices, our
14 JIP database is constructed as a joint project of REITI and the Hitotsubashi

University global COE program (Hi-Stat), and is available from the following website.
http://www.reiti.go.jp/jp/database/JIP2008/index.html
15 The issues of deflators are also discussed in Kato (2007).

12

model framework is considered reasonable.
Tables 1 and 2 present the results from estimating the LP, equation (12) (Melitz 1)
and (13) (Melitz 2) for both department stores and supermarkets, respectively. The
results of the tests if γ = 1 unless considering a bias,

σ −1, are in the bottom rows.
σ

The term “Variety” denotes the number of products. In our estimation, the floor space
per shop for each firm is used as a proxy of it. In both tables, the estimated coefficientson the intermediate input are unreliable except for two estimations, Melitz1 and 2 inTable 1 because they are statistically insignificant 16 . Therefore, we do not discuss them.
On the other hand, the coefficients on capital are significantly positive, save for the LP
in Table 1. It reveals that land should be included in the capital stocks in thisestimation 17 .
These tables show that the Wald tests do not reject the assumption of constantreturns to scale (CRS) in both department stores and supermarkets. Those results are,however, possibly biased because they do not include effects of the elasticity of
substitution between products. Therefore, we obtain the degree of bias from theestimated coefficients, and carry out a test of the following null hypothesis.

H0 :

σ
σ −1

(β k + β l + β e ) = 1

Since the coefficients on the term, [(rt − ~pt ) − nt ] are significantly positive while thoseon [(rt − ~p t ) − mt ] are negative, we calculate the degree of bias using the former ones.
16 We examined some slightly different forms of intermediate inputs as well. But none ofthem is significantly estimated.
17 We also estimated the production function where capital stock does not include theland, but the estimates were insignificant.

13

According to the results of it, the p-value of the Wald tests on the CRS assumption are
0.005 (department stores) and 0.084 (supermarkets), respectively. That is, the null
hypothesis that returns to scale are constant is rejected at the one and ten percent levels.
It indicates that the validity of the CRS assumption is significantly controversial in the
study of productivity at least in the retail trade industry if products are differentiated.
The estimated coefficient on the variable, Variety, is significantly positive forsupermarkets. It reveals that product differentiation has a positive effect on firms’
revenue. With quality adjusted productivity, it is positively associated with theestimated total factor productivity (TFP) in conventional approaches. On the other hand,
the term, Variety, is insignificantly estimated for department stores. It indicates thatdepartment stores and supermarkets follow different business models as is well known18 .
These results indicate that the industrial policy which is helpful for pursuing economies
of scale and product differentiation contributes to productivity growth of supermarkets.
Relating to the above issue, we discuss the effects of regulatory reforms on
productivity. Among various industrial policies, regulatory reform, in particularderegulation, is usually considered as important instruments to promote a favourable
economic environment. In 2000, the Japanese government enacted the Large-Scale
Retail Store Location Law in order to liberalise location for large scale retail stores.
From the above empirical results, this regulatory reform is expected to have a positiveeffect on productivity as a whole 19 . To test for the effect, we add a dummy variablewhich equals zero until 1999 and one after 2000 and re-examine the revenue functions 20 .
18 Department Stores are thought to provide their differentiated services throughvarious tenants such as high-class boutiques as well as their own service. In thismeaning, the number of tenants per commercial establishment is possibly a betterproxy although it is not examined because of data absence.
19 Our data do not include small businesses.
20 Since our data are relatively small, it is difficult to reasonably detect any pattern in a

14

The results are presented in Tables 3. In the tables the estimated coefficients on the
deregulation dummies are significantly positive at the one percent level. Although thisdummy variable contains not only effects of the deregulation but also all the economic
environments varying before and after the millennium, the positive estimates still imply
that the regulatory reform possibly contributed to improvement of productivity.
The above results indicate that the production function with the monopolisticcompetitive structure can be a useful instrument for estimating productivity anddiscussing desirable industrial policies.

5. Concluding Remarks
This paper examines returns to scale, productivity, and product differentiation using thefirm-level data of department stores and supermarkets in Japan between 1995 and 2004.
Following Melitz, we incorporate a monopolistic competitive structure into the
production function, and compare the results from those of a conventional approach. In
this study, our findings are as follows. First, the CRS assumption is controversial inempirics of production function of the retail trade industries. In both industries, thealternative assumption that the degree of returns to scale is not equal to unity is notstatistically rejected in the bias corrected estimates. It implies that the CRS assumption
should be carefully examined in the estimation of productivity since otherwise theestimated productivity might be biased. Secondly, product differentiation seems to givea positive contribution to productivity of supermarkets although it is not detected for
department stores. This result suggests that future research should apply this approachto other industries using reliable proxies of product variety because productdynamics of their average productivity levels.

15

differentiation is an important in many other industries as well. Thirdly, the regulatory
reform in 2000 seems to promote productivity growth in both forms of large-scale retailtraders. These results give a policy implication that the industrial policies which
promote economies of scale and product differentiation are favourable for the retailtrade industry.

Appendix: Descriptive Statistics of Product Differentiation

Max
Min
Ave
Med
Std
Skw
SampleDepartment
253490.00
1245.25
21266.55
16869.00
20768.57
3.95
900

Supermarket
141323.00
43.15
2406.101235.395703.38
14.20
1606

The gaps of the floor space per shop between firms are significantly huge for both
department stores and supermarkets. For both business models, data are considerably
skewed toward the lowest range.

16

References

Blanchard O. J., and N. Kiyotaki (1987), “Monopolistic Competition and the Effects ofAggregate Demand”, American Economic Review, 77, 647-666

Cooper R. and A. Johri (1997), “Dynamic Complementarities: A Quantitative Analysis”,
Journal of Monetary Economics, 40, 97-119

Holtz-Eakin D. and M. E. Lovely (1996), “Scale Economies, Returns to Variety and theProductivity of Public Capital”, Regional Science and Urban Economics, 26,
105-123

Kato A. (2007), “Survey on Productivity in the Service Sector (in Japanese)”, RIETI
Policy Discussion Paper, 07-P-005

Kim Y. G., H. U. Kwon and K. Fukao (2007), “Entry and Exit of Companies andEstablishments, and Productivity at the Industry Level (in Japanese)”, RIETI
Discussion Paper, 07-J-022

Kiyota K. and T. Matsuura (2004), “Construction and Usage of A Panel Data of ‘the
Basic Survey of the Business Structure and Activity’: Problems in Application to
Economic Analysis and Arrangement of Data (in Japanese)”, RIETI Policy
Discussion Paper, 04-P-004

17

Klette T. J. and Z. Griliches (1996), “The Inconsistency of Common Scale Estimators
When Output Prices Are Unobserved and Endogenous”, Journal of Applied
Econometrics, 11, 343-361.

Krugman P. R. (1990), The Age of Diminished Expectations, MIT Press, MA

Levinsohn J. and A. Petrin (2003), “Estimating Production Functions Using Inputs toControl for Unobservables”, Review of Economic Studies, 70 (2), 317-342

Loecker J. D. (2007), “Product Differentiation, Multi-Product Firms and Estimating the
Impact of Trade Liberalization on Productivity”, NBER Working Paper, No. 13155

Melitz M. J. (2000), “Estimating Firm-Level Productivity in Differentiated ProductIndustries”, Harvard, mimeo

Olley S., and A. Pakes (1996), “The Dynamics of Productivity in the
Telecommunication Equipment Industry”, Econometrica, 64, 1263-1297

Souza S. De (2006), “ Levinsohn and Petrin’s (2003) Methodology Works underMonopolistic Competition”, Economics Bulletin, 12 (6), 1-11

Tokui J., T. Inui and Y. G. Kim (2007), “The Embodied Technical Progress and the
Average Vintage of Capital (in Japanese)”, RIETI Discussion Paper, 07-J-035

18

Table 1: Department Stores
Coefficients
CapitalLabourIntermedia te[(rt − ~pt ) − nt ]LP

Melitz1

Melitz2

0.065

0.422***

0.298***(0.088)(0.137)(0.109)0.260***

0.268***

0.258***(0.035)(0.033)(0.033)4.38e-24

0.543**

0.374**(0.105)(0.228)(0.189)0.601***(0.070)[(rt − ~pt ) − mt ]-0.246***(0.024)
0.014

Variety
Wald (P − value)(0.012)

0.000

0.434

0.771

Note: ***, **, ** are 1%, 5%, and 10% significanceStandard Errors are in Parentheses

Table 2: Supermarkets
Coefficients
CapitalLabourIntermedia te[(rt − p~t ) − nt ]LP

Melitz1

Melitz2

0.501***

0.733***

0.809***(0.181)(0.201)(0.234)0.289***

0.269***

0.283***(0.022)(0.024)(0.027)

0.020

0.110

0.161

(0.122)(0.152)(0.232)0.282***(0.057)[(rt − p~t ) − mt ]-0.218***(0.080)0.017**

Variety
Wald (P − value)(0.008)

0.306

0.624

0.244

Note: ***, **, ** are 1%, 5%, and 10% significanceStandard Errors are in Parentheses

19

Table 3: Revenue Function with the Deregulation Dummy
Coefficients
CapitalDepartSuper

0.429***(0.104)0.691***(0.174)

Labour

0.265***(0.032)0.274***(0.025)Intermediate

0.557***(0.196)7.65e-09(0.101)

Variety-0.178***(0.027)0.015

0.097*(0.054)0.017**

Dummy(0.010)0.090***(0.007)0.060***(0.012)(0.013)

0.298

0.412

[(rt − ~pt ) − m t ]Wald (P − value)

Note: ***, **, ** are 1%, 5%, and 10% significanceStandard Errors are in Parentheses