| Title: | Compute Price of Production and Labor Values |
| Version: | 1.0.0 |
| Description: | Computes the uniform rate of profit, the vector of price of production and the vector of direct prices; and also compute measures of deviation between market prices, direct prices and prices of production. <doi:10.1016/j.strueco.2026.03.009>. You provide the input-output data and 'clptheory' does the calculations for you. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Imports: | popdemo, stats, dplyr, magrittr |
| Depends: | R (≥ 2.10) |
| LazyData: | true |
| Suggests: | knitr, rmarkdown |
| URL: | https://github.com/dbasu-umass/clptheory/ |
| NeedsCompilation: | no |
| Packaged: | 2026-03-18 00:25:55 UTC; dbasu |
| Author: | Deepankar Basu [aut, cre, cph] |
| Maintainer: | Deepankar Basu <dbasu@umass.edu> |
| Repository: | CRAN |
| Date/Publication: | 2026-03-18 00:40:02 UTC |
AUS IO Table
Description
Input Output Tables for the Australian economy from the World Input Output Database.
Usage
ausiot
Format
Input Output table for Australia for 15 years, 2000-2014.
Source
Examples
ausiot[1:3,1:3]
Socio Economic Accounts
Description
This is the socio economic accounts for the Australian economy extracted from the 2016 release of the World Input Output Database. It contains industry-level data on employment, capital stocks, gross output and value added at current and constant prices, in millions of local currency. The industry classification is consistent with the world input-output tables.
Usage
aussea
Format
A industry-level (53 industries) data set for Australia over 15 years, 2000-2014.
- country
Country code.
- code
Industry code.
- description
Description of the industry.
- variable
One of the following variables:
- GO
Gross output by industry at current basic prices (in millions of national currency).
- II
Intermediate inputs at current purchasers' prices (in millions of national currency).
- VA
Gross value added at current basic prices (in millions of national currency).
- EMP
Number of persons engaged (thousands).
- EMPE
Number of employees (thousands).
- H_EMPE
Total hours worked by employees (millions).
- COMP
Compensation of employees (in millions of national currency).
- LAB
Labour compensation (in millions of national currency).
- CAP
Capital compensation (in millions of national currency).
- K
Nominal capital stock (in millions of national currency).
- GO_PI
Price levels gross output, 2010=100.
- II_PI
Price levels of intermediate inputs, 2010=100.
- VA_PI
Price levels of gross value added, 2010=100.
- GO_QI
Gross output, volume indices, 2010=100.
- II_QI
Intermediate inputs, volume indices, 2010=100.
- VA_QI
Value added, volume indices, 2010=100.
- NOMEXCH
Nominal exchange rate between the national currency and the US dollar.
Source
Examples
summary(aussea$COMP)
Create data set for analysis.
Description
This function creates the data objects (matrices, vectors and scalars) necessary to implement the SI and NI from the WIOD.
Usage
createdata(country, year, datasea, dataio)
Arguments
country |
country code as a character (e.g. "USA"). |
year |
year (eg. 2000). |
datasea |
the socio economic accounts (data frame). |
dataio |
the input-output (data frame). |
Value
A list with the following elements:
Ahat |
The input-output matrix |
l |
The direct labor input vector (complex labor) |
l_simple |
The direct labor input vector (simple labor) |
Q |
The gross output vector |
wavg |
The average or uniform nominal wage rate |
wagevector_all |
The vector of nominal wage rates |
vlp |
Value of labor power |
b |
Real wage bundle (consumption/total hours) |
b1 |
Real wage bundle (share of PCE * min wage) |
pshare |
Average profit share |
Examples
createdata(country="USA",year=2010,datasea=usasea,dataio=usaiot)
Nonregression-based measures of distance between MP, DP, PP
Description
This function computes different measures of distance between prices of production (PP), market prices (MP) and direct prices (DP).
Usage
nonregdist(x, y, w, w_avg, Q)
Arguments
x |
price of production vector (1 x n). |
y |
direct prices vector (1 x n). |
w |
vector of nominal wage rates (1 x n). |
w_avg |
average wage rate (scalar). |
Q |
gross output vector (1 x n) |
Value
A list with the following elements:
rmseppmp |
RMSE between price of production and market prices |
rmsedpmp |
RMSE between direct prices and market prices |
rmseppdp |
RMSE between prices of production and direct prices |
madppmp |
MAD between price of production and market prices |
maddpmp |
MAD between direct prices and market prices |
madppdp |
MAD between prices of production and direct prices |
mawdppmp |
MAWD between price of production and market prices |
mawddpmp |
MAWD between direct prices and market prices |
mawdppdp |
MAWD between prices of production and direct prices |
angleppmp |
Angle between price of production and market prices |
angledpmp |
Angle between direct prices and market prices |
angleppdp |
Angle between prices of production and direct prices |
ddistppmp |
D-distance between price of production and market prices |
ddistdpmp |
D-distance between direct prices and market prices |
ddistppdp |
D-distance between prices of production and direct prices |
Examples
# ------ Data
# price of production vector
x<- matrix(
data = c(0.25, 0.50, 0.75),
nrow=1
)
# direct price vector
y <- matrix(
data = c(0.33, 0.275, 0.85),
ncol=1
)
# Gross output vector
Q <- matrix(
data = c(26530, 18168, 73840),
ncol=1
)
# nominal wage rate vector
w <- matrix(
data = c(0.5, 0.33, 0.75),
ncol=1
)
# average wage (scalar)
w_avg <- 0.66
# Compute prices of production
nonregdist(x = x, y = y, Q = Q, w = w, w_avg = w_avg)
Circulating capital model using the New Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a basic circulating capital model using the New Interpretation.
Usage
ppnewint1(A, w, v, Q, l_simple)
Arguments
A |
input-output matrix (n x n). |
w |
uniform nominal wage rate (scalar). |
v |
value of labor power (scalar) |
Q |
gross output vector (n x 1). |
l_simple |
vector of simple labor input (1 x n). |
Value
A list with the following elements:
meig |
Maximum eigen value of A |
urop |
Uniform rate of profit (as a fraction) |
mrop |
Maximum rate of profit (as a fraction) |
pp |
Price of production vector |
dp |
Direct prices |
lvalues |
Labor values vector |
Anonneg |
Is A Nonnegative? (1=Y,0=N) |
Airred |
Is A Irreducible? (1=Y,0=N) |
Examples
# ------ Data
# Input-output matrix
A <- matrix(
data = c(0.265,0.968,0.00681,0.0121,0.391,0.0169,0.0408,0.808,0.165),
nrow=3, ncol=3, byrow = TRUE
)
# Direct labor input vector (complex)
l <- matrix(
data = c(0.193, 3.562, 0.616),
nrow=1
)
# Real wage bundle
b <- matrix(
data = c(0.0109, 0.0275, 0.296),
ncol=1
)
# Gross output vector
Q <- matrix(
data = c(26530, 18168, 73840),
ncol=1
)
# Direct labor input vector (simple)
l_simple <- l
# Market price vector
m <- matrix(data = c(4, 60, 7),nrow=1)
# Uniform nominal wage rate
wavg <- m%*%b
# Value of labor power
v <- 2/3
# Compute prices of production
ppnewint1(A = A,w = wavg[1,1],v=v,Q = Q,l_simple = l)
Capital stock model using the New Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a capital stock model using the New Interpretation.
Usage
ppnewint2(A, l, w, v, Q, D, K, t, Tax)
Arguments
A |
input-output matrix (n x n). |
l |
vector of simple labor input (1 x n). |
w |
average nominal wage rate (scalar) |
v |
value of labor power (scalar) |
Q |
gross output vector (n x 1). |
D |
depreciation matrix (n x n). |
K |
capital stock coefficient matrix (n x n). |
t |
diagonal matrix of turnover rates (n x n). |
Tax |
matrix of tax rates (n x n). |
Value
A list with the following elements:
meig |
Maximum eigen value of A |
urop |
Uniform rate of profit (as a fraction) |
mrop |
Maximum rate of profit (as a fraction) |
pp |
Price of production vector |
dp |
Direct prices |
lvalues |
Labor values vector |
Mnonneg |
Is M Nonnegative? (1=Y,0=N) |
Mirred |
Is M Irreducible? (1=Y,0=N) |
Nnonneg |
Is N Nonnegative? (1=Y,0=N) |
Nirred |
Is N Irreducible? (1=Y,0=N) |
MNirred |
Is M and N both Irreducible? (1=Y,0=N) |
Examples
# ------ Data
# Input-output matrix
A <- matrix(
data = c(0.265,0.968,0.00681,0.0121,0.391,0.0169,0.0408,0.808,0.165),
nrow=3, ncol=3, byrow = TRUE
)
# Depreciation matrix
D <- matrix(
data = c(0,0,0,0.00568,0.0267,0.0028,0.00265,0.0147,0.00246),
nrow = 3, ncol = 3, byrow = TRUE
)
# Direct labor input vector (complex)
l <- matrix(
data = c(0.193, 3.562, 0.616),
nrow=1
)
# Value of labor power
v <- 2/3
# Gross output vector
Q <- matrix(
data = c(26530, 18168, 73840),
ncol=1
)
# Gross output vector
Q <- matrix(
data = c(26530, 18168, 73840),
ncol = 1
)
# Capital stock coefficient matrix
K <- matrix(
data = c(0,0,0,0.120,0.791,0.096,0.037,0.251,0.043),
nrow=3, ncol=3, byrow=TRUE
)
# Diagonal matrix of turnover rates
t <- diag(c(0.317, 0.099, 0.187))
# Matrix of tax rates (assumed 0 for this example)
Tax <- matrix(0,nrow=3,ncol=3)
# Average nominal wage rate
w <- 3.765
# Compute prices of production
ppnewint2(A=A,l=l,w=w,v=v,Q=Q,D=D,K=K,t=t,Tax=Tax)
Circulating capital model using the Sraffian method.
Description
This function computes the uniform rate of profit, prices of production and labor values for a basic circulating capital model using the Sraffian method.
Usage
ppsraffa1(A, Q, pshare, l_simple)
Arguments
A |
input-output matrix (n x n). |
Q |
gross output vector (n x 1). |
pshare |
profit share (scalar) |
l_simple |
vector of simple labor input (1 x n). |
Value
A list with the following elements:
meig |
Maximum eigen value of A |
urop |
Uniform rate of profit (as a fraction) |
mrop |
Maximum rate of profit (as a fraction) |
ppabs |
Price of production vector (absolute) |
pprel |
Price of production vector (relative) |
lvalues |
Labor values vector |
mevn |
Monetary expression of value using net output |
mevg |
Monetary expression of value using gross output |
Anonneg |
Is A Nonnegative? (1=Y,0=N) |
Airred |
Is A Irreducible? (1=Y,0=N) |
Examples
# ------ Data
# Input-output matrix
A <- matrix(
data = c(0.265,0.968,0.00681,0.0121,0.391,0.0169,0.0408,0.808,0.165),
nrow=3, ncol=3, byrow = TRUE
)
# Direct labor input vector (complex)
l <- matrix(
data = c(0.193, 3.562, 0.616),
nrow=1
)
# Gross output vector
Q <- matrix(
data = c(26530, 18168, 73840),
ncol=1
)
# Direct labor input vector (simple)
l_simple <- l
# Profit share
pshare <- 1/3
# Compute prices of production
ppsraffa1(A = A,pshare=pshare,Q = Q,l_simple = l)
Circulating capital model using the Standard Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a basic circulating capital model using the Standard Interpretation.
Usage
ppstdint1(A, b, Q, l_simple)
Arguments
A |
input-output matrix (n x n). |
b |
vector real wage bundle (n x 1). |
Q |
gross output vector (n x 1). |
l_simple |
vector of simple labor input (1 x n). |
Value
A list with the following elements:
meig |
Maximum eigen value of M |
urop |
Uniform rate of profit (as a fraction) |
mrop |
Maximum rate of profit (as a fraction) |
pp |
Price of production vector |
dp |
Direct prices |
lvalues |
Labor values vector |
Mnonneg |
Is M Nonnegative? (1=Y,0=N) |
Mirred |
Is M Irreducible? (1=Y,0=N) |
Examples
# ------ Data
# Input-output matrix
A <- matrix(
data = c(0.265,0.968,0.00681,0.0121,0.391,0.0169,0.0408,0.808,0.165),
nrow=3, ncol=3, byrow = TRUE
)
# Direct labor input vector (complex)
l <- matrix(
data = c(0.193, 3.562, 0.616),
nrow=1
)
# Real wage bundle
b <- matrix(
data = c(0.0109, 0.0275, 0.296),
ncol=1
)
# Gross output vector
Q <- matrix(
data = c(26530, 18168, 73840),
ncol=1
)
# Direct labor input vector (simple)
l_simple <- l
# Compute prices of production
ppstdint1(A = A,b = b,Q = Q,l_simple = l)
Capital stock model using the Standard Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a capital stock model using the Standard Interpretation.
Usage
ppstdint2(A, l, b, Q, D, K, t, Tax)
Arguments
A |
input-output matrix (n x n). |
l |
vector of simple labor input (1 x n). |
b |
vector real wage bundle (n x 1). |
Q |
gross output vector (n x 1). |
D |
depreciation matrix (n x n). |
K |
capital stock coefficient matrix (n x n). |
t |
diagonal matrix of turnover rates (n x n). |
Tax |
matrix of tax rates (n x n). |
Value
A list with the following elements:
meig |
Maximum eigen value of M |
urop |
Uniform rate of profit (as a fraction) |
mrop |
Maximum rate of profit (as a fraction) |
pp |
Price of production vector |
dp |
Direct prices |
lvalues |
Labor values vector |
Mnonneg |
Is M Nonnegative? (1=Y,0=N) |
Mirred |
Is M Irreducible? (1=Y,0=N) |
Examples
# ------ Data
# Input-output matrix
A <- matrix(
data = c(0.265,0.968,0.00681,0.0121,0.391,0.0169,0.0408,0.808,0.165),
nrow=3, ncol=3, byrow = TRUE
)
# Depreciation matrix
D <- matrix(
data = c(0,0,0,0.00568,0.0267,0.0028,0.00265,0.0147,0.00246),
nrow = 3, ncol = 3, byrow = TRUE
)
# Direct labor input vector (complex)
l <- matrix(
data = c(0.193, 3.562, 0.616),
nrow=1
)
# Real wage bundle
b <- matrix(
data = c(0.0109, 0.0275, 0.296),
ncol=1
)
# Gross output vector
Q <- matrix(
data = c(26530, 18168, 73840),
ncol=1
)
# Gross output vector
Q <- matrix(
data = c(26530, 18168, 73840),
ncol = 1
)
# Capital stock coefficient matrix
K <- matrix(
data = c(0,0,0,0.120,0.791,0.096,0.037,0.251,0.043),
nrow=3, ncol=3, byrow=TRUE
)
# Diagonal matrix of turnover rates
t <- diag(c(0.317, 0.099, 0.187))
# Matrix of tax rates (assumed 0)
Tax <- matrix(0,nrow=3,ncol=3)
# Compute prices of production
ppstdint2(A=A,l=l,b=b,Q=Q,D=D,K=K,t=t,Tax=Tax)
USA IO Table
Description
Input Output Tables for the US economy from the World Input Output Database.
Usage
usaiot
Format
Input Output table for USA for 15 years, 2000-2014.
Source
Examples
usaiot[1:5,1:5]
Real Wage Bundle, USA
Description
Personal Consumption Expenditure from the Input Output Table for the USA. This data is used to construct the real wage bundle for computing the price of production vector.
Usage
usarwb
Format
Consumption expenditure on the output of 53 industries for USA for 15 years, 2000-2014.
Source
Examples
data(usarwb)
Socio Economic Accounts
Description
This is the socio economic accounts for the USA extracted from the 2016 release of the World Input Output Database. It contains industry-level data on employment, capital stocks, gross output and value added at current and constant prices, in millions of local currency. The industry classification is consistent with the world input-output tables.
Usage
usasea
Format
A industry-level (53 industries) data set for USA over 15 years, 2000-2014.
- country
Country code.
- code
Industry code.
- description
Description of the industry.
- variable
One of the following variables:
- GO
Gross output by industry at current basic prices (in millions of national currency).
- II
Intermediate inputs at current purchasers' prices (in millions of national currency).
- VA
Gross value added at current basic prices (in millions of national currency).
- EMP
Number of persons engaged (thousands).
- EMPE
Number of employees (thousands).
- H_EMPE
Total hours worked by employees (millions).
- COMP
Compensation of employees (in millions of national currency).
- LAB
Labour compensation (in millions of national currency).
- CAP
Capital compensation (in millions of national currency).
- K
Nominal capital stock (in millions of national currency).
- GO_PI
Price levels gross output, 2010=100.
- II_PI
Price levels of intermediate inputs, 2010=100.
- VA_PI
Price levels of gross value added, 2010=100.
- GO_QI
Gross output, volume indices, 2010=100.
- II_QI
Intermediate inputs, volume indices, 2010=100.
- VA_QI
Value added, volume indices, 2010=100.
- NOMEXCH
Nominal exchange rate between the national currency and the US dollar.
Source
Examples
summary(usasea$COMP)