| Title: | Compute Price of Production and Labor Values |
| Version: | 0.1.0 |
| Description: | Computes the uniform rate of profit, the vector of price of production and the vector of labor values; and also compute measures of deviation between relative prices of production and relative values. https://scholarworks.umass.edu/econ_workingpaper/347/. You provide the input-output data and 'clptheory' does the calculations for you. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| Imports: | popdemo, stats, car, utils, dplyr, magrittr |
| Depends: | R (≥ 2.10) |
| LazyData: | true |
| Suggests: | knitr, rmarkdown |
| URL: | https://github.com/dbasu-umass/clptheory/ |
| NeedsCompilation: | no |
| Packaged: | 2023-04-03 13:46:43 UTC; basu15 |
| Author: | Deepankar Basu [aut, cre, cph] |
| Maintainer: | Deepankar Basu <dbasu@umass.edu> |
| Repository: | CRAN |
| Date/Publication: | 2023-04-04 11:40:06 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.
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 |
The consumption or real wage bundle |
pshare |
Average profit share |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
Examples
createdata(country="USA",year=2010,datasea=usasea,dataio=usaiot)
Nonregression-based Measures of Deviation.
Description
This function computes various non-regression based measures of deviation between the vector of all possible relative labor values and the vector of all possible relative prices of production.
Usage
nregtestrel(x, y, w, w_avg, mev, Q)
Arguments
x |
price vector (1 x n). |
y |
value vector (1 x n). |
w |
nominal wage rate vector (1 x n). |
w_avg |
average nominal wage rate (scalar) |
mev |
monetary expression of value using gross output (scalar) |
Q |
gross output vector (n x 1). |
Value
A list with the following elements:
rmse |
Root mean squared error |
mad |
Mean absolute distance |
mawd |
Mean absolute weighted distance |
cdm |
Classical distance measure |
angle |
Angle between the two vectors (in degrees) |
distangle |
Distance computed using the angle |
lrelpplv |
Length of the relative price of production (or labor value) vector |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
Examples
# 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
# Vector of nominal wage rates
w <- matrix(data=rep(wavg,3),nrow=1)
# Value of labor power
v <- 2/3
# Compute prices of production using NI
ni1 <- ppnewint1(A = A,l = l,w = wavg[1,1],v=v,Q = Q,l_simple = l)
# Nonregression-based measures of deviation
nregtestrel(x=ni1$ppabs,y=ni1$lvalues,w=w,w_avg=wavg[1,1],mev=ni1$mevg,Q=Q)
Circulating capital model 1 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. The model has uniform wage rates across industries and does not take account of unproductive labor for labor value calculations.
Usage
ppnewint1(A, l, w, v, Q, l_simple)
Arguments
A |
input-output matrix (n x n). |
l |
vector of complex labor input (1 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) |
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) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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,l = l,w = wavg[1,1],v=v,Q = Q,l_simple = l)
Circulating capital model 2 using the New Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a circulating capital model using the New Interpretation. The model allows differential wage rates across industries but does not take account of unproductive labor for labor value calculations.
Usage
ppnewint2(A, l, w, v, Q, l_simple)
Arguments
A |
input-output matrix (n x n). |
l |
vector of complex labor input (1 x n). |
w |
vector of nominal wage rates (1 x n). |
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) |
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) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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 wage rate
wavg <- m%*%b
# Vector of nominal wage rates
w <- matrix(data=c(wavg-0.5,wavg,wavg+0.5),nrow=1)
# Value of labor power
v <- 2/3
# Compute prices of production
ppnewint2(A = A,l = l,w = w[1,],v=v,Q = Q,l_simple = l)
Circulating capital model 3 using the New Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a circulating capital model using the New Interpretation. The model has uniform wage rates across industries and takes account of unproductive labor for labor value calculations.
Usage
ppnewint3(A, Ap, l, lp, w, v, Q, Qp, lp_simple)
Arguments
A |
input-output matrix (n x n). |
Ap |
input-output matrix for the subset of productive industries (m x m). |
l |
vector of complex labor input (1 x n). |
lp |
vector of complex labor input for the subset of productive industries (1 x m). |
w |
uniform nominal wage rate (scalar). |
v |
value of labor power (scalar). |
Q |
gross output vector (n x 1). |
Qp |
gross output vector for the subset of productive industries (m x 1). |
lp_simple |
vector of simple labor input for the subset of productive industries (1 x m). |
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) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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 <- 3/5
# Compute prices of production
ppnewint3(A=A,Ap=A[1:2,1:2],l=l,lp=l[1,1:2],w=wavg[1,1],v=v,Q=Q,Qp=Q[1:2,1],lp_simple=l[1,1:2])
Circulating capital model 4 using the New Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a circulating capital model using the New Interpretation. The model allows differential wage rates across industries and takes account of unproductive labor for labor value calculations.
Usage
ppnewint4(A, Ap, l, lp, w, wp, v, Q, Qp, lp_simple)
Arguments
A |
input-output matrix (n x n). |
Ap |
input-output matrix for the subset of productive industries (m x m). |
l |
vector of complex labor input (1 x n). |
lp |
vector of complex labor input for the subset of productive industries (1 x m). |
w |
vector of nominal wage rates (1 x n). |
wp |
vector of nominal wage rates for the subset of productive industries (1 x m). |
v |
value of labor power (scalar). |
Q |
gross output vector (n x 1). |
Qp |
gross output vector for the subset of productive industries (m x 1). |
lp_simple |
vector of simple labor input for the subset of productive industries (1 x m). |
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) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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 wage rate
wavg <- m%*%b
# Vector of nominal wage rates
w <- matrix(data=c(wavg-0.5,wavg,wavg+0.5),nrow=1)
# Value of labor power
v <- 3/5
# Compute prices of production
ppnewint4(A=A,Ap=A[1:2,1:2],l=l,lp=l[1,1:2],w=w[1,],wp=w[1,1:2],v=v,
Q=Q,Qp=Q[1:2,1],lp_simple=l[1,1:2])
Capital stock model 1 using the New Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a basic capital stock model using the New Interpretation. The model has uniform wage rates across industries and does not take account of unproductive labor for labor value calculations.
Usage
ppnewint5(A, l, w, v, Q, D, K, t, l_simple)
Arguments
A |
input-output matrix (n x n). |
l |
vector of complex labor input (1 x n). |
w |
uniform 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 |
turnover times matrix (n x n diagonal). |
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 |
Nnonneg |
Is N Nonnegative? (1=Y,0=N) |
Nirred |
Is N Irreducible? (1=Y,0=N) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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
# 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
)
# 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 turnover matrix
t <- diag(c(0.317, 0.099, 0.187))
# Compute prices of production
ppnewint5(A = A,l = l,w = wavg[1,1],v=v,Q = Q,l_simple = l,D=D,K=K,t=t)
Capital stock model 2 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. The model allows differential wage rates across industries but does not take account of unproductive labor for labor value calculations.
Usage
ppnewint6(A, l, w, v, Q, D, K, t, l_simple)
Arguments
A |
input-output matrix (n x n). |
l |
vector of complex labor input (1 x n). |
w |
vector of nominal wage rates (1 x n). |
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 |
turnover times matrix (n x n diagonal). |
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 |
Nnonneg |
Is N Nonnegative? (1=Y,0=N) |
Nirred |
Is N Irreducible? (1=Y,0=N) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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
# Vector of nominal wage rates
w <- matrix(data=c(wavg-0.5,wavg,wavg+0.5),nrow=1)
# Value of labor power
v <- 2/3
# 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
)
# 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 turnover matrix
t <- diag(c(0.317, 0.099, 0.187))
# Compute prices of production
ppnewint6(A=A,l=l,w=w[1,],v=v,Q=Q,l_simple=l,D=D,K=K,t=t)
Capital stock model 3 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. The model has uniform wage rates across industries and takes account of unproductive labor for labor value calculations.
Usage
ppnewint7(A, Ap, l, lp, w, v, Q, Qp, D, Dp, K, t, lp_simple)
Arguments
A |
input-output matrix (n x n). |
Ap |
input-output matrix for the subset of productive industries (m x m). |
l |
vector of complex labor input (1 x n). |
lp |
vector of complex labor input for the subset of productive industries (1 x m). |
w |
uniform nominal wage rate (scalar). |
v |
value of labor power (scalar). |
Q |
gross output vector (n x 1). |
Qp |
gross output vector for the subset of productive industries (m x 1). |
D |
depreciation matrix (n x n). |
Dp |
depreciation matrix for the subset of productive industries (m x m). |
K |
capital stock coefficient matrix (n x n). |
t |
turnover times matrix (n x n diagonal). |
lp_simple |
vector of simple labor input for the subset of productive industries (1 x m). |
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 |
Nnonneg |
Is N Nonnegative? (1=Y,0=N) |
Nirred |
Is N Irreducible? (1=Y,0=N) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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
# Vector of nominal wage rates
w <- matrix(data=c(wavg-0.5,wavg,wavg+0.5),nrow=1)
# Value of labor power
v <- 3/5
# 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
)
# 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 turnover matrix
t <- diag(c(0.317, 0.099, 0.187))
# Compute prices of production
ppnewint7(A=A,Ap=A[1:2,1:2],l=l,lp=l[1,1:2],w=wavg[1,1],v=v,
Q=Q,Qp=Q[1:2,1],lp_simple=l[1,1:2],D=D,Dp=D[1:2,1:2],K=K,t=t)
Capital stock model 4 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. The model allows differential wage rates across industries and takes account of unproductive labor for labor value calculations.
Usage
ppnewint8(A, Ap, l, lp, w, wp, v, Q, Qp, D, Dp, K, t, lp_simple)
Arguments
A |
input-output matrix (n x n). |
Ap |
input-output matrix for the subset of productive industries (m x m). |
l |
vector of complex labor input (1 x n). |
lp |
vector of complex labor input for the subset of productive industries (1 x m). |
w |
vector of nominal wage rates (1 x n). |
wp |
vector of nominal wage rates for the subset of productive industries (1 x m). |
v |
value of labor power (scalar). |
Q |
gross output vector (n x 1). |
Qp |
gross output vector for the subset of productive industries (m x 1). |
D |
depreciation matrix (n x n). |
Dp |
depreciation matrix for the subset of productive industries (m x m). |
K |
capital stock coefficient matrix (n x n). |
t |
turnover times matrix (n x n diagonal). |
lp_simple |
vector of simple labor input for the subset of productive industries (1 x m). |
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 |
Nnonneg |
Is N Nonnegative? (1=Y,0=N) |
Nirred |
Is N Irreducible? (1=Y,0=N) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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
# Vector of nominal wage rates
w <- matrix(data=c(wavg-0.5,wavg,wavg+0.5),nrow=1)
# Value of labor power
v <- 3/5
# 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
)
# 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 turnover matrix
t <- diag(c(0.317, 0.099, 0.187))
# Compute prices of production
ppnewint8(A=A,Ap=A[1:2,1:2],l=l,lp=l[1,1:2],w=w[1,],wp=w[1,1:2],v=v,
Q=Q,Qp=Q[1:2,1],lp_simple=l[1,1:2],D=D,Dp=D[1:2,1:2],K=K,t=t)
Circulating capital model 1 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. The model has uniform wage rates across industries and does not take into account unproductive labor for labor value calculations.
Usage
ppstdint1(A, l, b, Q, l_simple)
Arguments
A |
input-output matrix (n x n). |
l |
vector of complex labor input (1 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) |
ppabs |
Price of production vector (absolute) |
pprel |
Price of production vector (relative) |
lvalues |
Labor values vector |
dprice |
Direct price vector |
mevg |
Monetary expression of value using gross output |
mnonneg |
Is M Nonnegative? (1=Y,0=N) |
mirred |
Is M Irreducible? (1=Y,0=N) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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,l = l,b = b,Q = Q,l_simple = l)
Circulating capital model 2 using the Standard Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a circulating capital model using the Standard Interpretation. The model has uniform wage rates across industries and takes into account unproductive labor for labor value calculations.
Usage
ppstdint2(A, Ap, l, b, Q, Qp, lp_simple)
Arguments
A |
input-output matrix (n x n). |
Ap |
input-output matrix for the subset of productive industries (m x m). |
l |
vector of complex labor input (1 x n). |
b |
vector real wage bundle (n x 1). |
Q |
gross output vector (n x 1). |
Qp |
gross output vector for the subset of productive industries (m x 1). |
lp_simple |
vector of simple labor input for the subset of productive industries (1 x m). |
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) |
ppabs |
Price of production vector (absolute) |
pprel |
Price of production vector (relative) |
lvalues |
Labor values vector |
dprice |
Direct price vector |
mevg |
Monetary expression of value using gross output |
mnonneg |
Is M Nonnegative? (1=Y,0=N) |
mirred |
Is M Irreducible? (1=Y,0=N) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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
ppstdint2(A=A,Ap=A[1:2,1:2],l=l,b=b,Q=Q,Qp=Q[1:2,1],lp_simple=l[1,1:2])
Capital stock model 1 using the Standard Interpretation.
Description
This function computes the uniform rate of profit, prices of production and labor values for a basic capital stock model using the Standard Interpretation. The model has uniform wage rates across industries and does not take into account unproductive labor for labor value calculations.
Usage
ppstdint3(A, l, b, Q, D, K, t, l_simple)
Arguments
A |
input-output matrix (n x n). |
l |
vector of complex 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 |
turnover matrix (n x n diagonal matrix). |
l_simple |
vector of simple labor input (1 x n). |
Value
A list with the following elements:
meig |
Maximum eigen value of N |
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 |
dprice |
Direct price vector |
mevg |
Monetary expression of value using gross output |
nnonneg |
Is N Nonnegative? (1=Y,0=N) |
nirred |
Is N Irreducible? (1=Y,0=N) |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
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
# 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
)
# 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 turnover matrix
t <- diag(c(0.317, 0.099, 0.187))
# Compute prices of production
ppstdint3(A = A,l = l,b = b,Q = Q,l_simple = l,D=D,K=K,t=t)
Regression-based Measures of Deviation.
Description
This function computes various regression based measures of deviation between the vector of all possible relative labor values and the vector of all possible relative prices of production. It runs a log-log and a level-level regression of relative prices on relative values and tests the joint null hypothesis that the intercept is 0 and the slope is 1.
Usage
regtestrel(x, y)
Arguments
x |
price vector (1 x n). |
y |
value vector (1 x n). |
Value
A list with the following elements:
a0lg |
Intercept in the log-log regression |
a1lg |
Slope in the log-log regression |
r2lg |
R-squared in the log-log regression |
fstatlg |
F-stat of the null hypothesis that a0=0 and a1=1 in the log-log regression |
pvallg |
P-value of the null hypothesis that a0=0 and a1=1 in the log-log regression |
nlg |
Number of observations in the log-log regression |
a0lv |
Intercept in the level-level regression |
a1lv |
Slope in the level-level regression |
r2lv |
R-squared in the level-level regression |
fstatlv |
F-stat of the null hypothesis that a0=0 and a1=1 in the level-level regression |
pvallv |
P-value of the null hypothesis that a0=0 and a1=1 in the level-level regression |
nlv |
Number of observations in the level-level regression |
References
Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/
Examples
# 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
# Vector of nominal wage rates
w <- matrix(data=rep(wavg,3),nrow=1)
# Value of labor power
v <- 2/3
# Compute prices of production using NI
ni1 <- ppnewint1(A = A,l = l,w = wavg[1,1],v=v,Q = Q,l_simple = l)
# Regression-based measures of deviation
regtestrel(x=ni1$ppabs,y=ni1$lvalues)
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)