clptheory

The goal of clptheory (classical price theory) is to create a suite of functions to implement the classical theory of prices. The functions in this package computes the uniform rate of profit, the vector of price of production and the vector of labor values for different specifications of the circulating capital model and the capital stock model. The functions also computes various regression- and non-regression-based measures of deviation between the vector of all possible relative prices of production and the vector of all possible relative labor values.

Installation

You can install the package clptheory from CRAN with:

# Uncomment the following line
# install.packages("clptheory")

You can install the development version of clptheory from GitHub with:

# Uncomment the following two lines
# install.packages("devtools")
# devtools::install_github("dbasu-umass/clptheory")

Main Functions

This package provides the following functions.

ppstdint1: a function to estimate a basic circulating capital model (uniform wage rates across industries + not taking account of unproductive industries) with the Standard Interpretation;
ppstdint2: a function to estimate a circulating capital model (uniform wage rates across industries + takes account of unproductive industries) with the Standard Interpretation;
ppstdint3: a function to estimate a basic capital stock model (uniform wage rates across industries + not taking account of unproductive industries) with the Standard Interpretation;
ppnewint1: a function to estimate a basic circulating capital model (uniform wage rates across industries + not taking account of unproductive industries) with the New Interpretation;
ppnewint2: a function to estimate a circulating capital model (allows differential wage rates across industries + not taking account of unproductive industries) with the New Interpretation;
ppnewint3: a function to estimate a circulating capital model (uniform wage rates across industries + takes account of unproductive industries) with the New Interpretation;
ppnewint4: a function to estimate a circulating capital model (allows differential wage rates across industries + takes account of unproductive industries) with the New Interpretation;
ppnewint5: a function to estimate a basic capital stock model (uniform wage rates across industries + not taking account of unproductive industries) with the New Interpretation;
ppnewint6: a function to estimate a capital stock model (allows differential wage rates across industries + not taking account of unproductive industries) with the New Interpretation;
ppnewint7: a function to estimate a capital stock model (uniform wage rates across industries + takes account of unproductive industries) with the New Interpretation;
ppnewint8: a function to estimate a capital stock model (allows differential wage rates across industries + takes account of unproductive industries) with the New Interpretation;
nregtestrel: a function that computes various non-regression-based measures of deviation between the vector of relative prices of production and the vector of relative labor values;
regtestrel: a function that computes various regression-based measures of deviation between the vector of relative prices of production and the vector of relative labor values;
createdata: a function to create the data objects (matrices, vectors and scalars) necessary to implement the SI and NI.

The package contains the following three datasets.

aussea: the socio economic accounts for the Australian economy extracted from the 2016 release of the World Input Output Database; this data set contains industry-level variables (53 industries) for the USA for 15 years, 2000-2014;
ausiot: input-output tables for the Australian economy extracted from the 2016 release of the World Input Output Database; this data set contains 53-industry input-output tables for the USA for 15 years, 2000-2014;
usasea: the socio economic accounts for the USA extracted from the 2016 release of the World Input Output Database; this data set contains industry-level variables (53 industries) for the USA for 15 years, 2000-2014;
usaiot: input-output tables for the USA extracted from the 2016 release of the World Input Output Database; this data set contains 53-industry input-output tables for the USA for 15 years, 2000-2014;
usarwb: personal consumption expenditure on the output of the 53 industries of the input-output tables for the USA extracted from the 2016 release of the World Input Output Database; this data set contains data for 15 years, 2000-2014. (Note: This data set is not necessary for the analysis.)

Example 1: Analysis for Australia

Let us conduct price of production analysis for Australia (AUS) and see how to use the functions in clptheory to

compute the uniform rate of profit and the vectors of labor values and prices of production for a basic circulating capital model using the Standard Interpretation and the New Interpretation; and
compute regression- and non-regression-based measures of deviation between the vector of all possible relative prices of production and the vector of all possible relative labor values.

Let us load the package.

# Load library
library(clptheory)

Data

Let us create the data objects.

ausdata <- clptheory::createdata(
  country = "AUS", year = 2010, 
  datasea = aussea, dataio = ausiot
  )
#> c("C33", "M71", "M72", "M73", "M74_M75", "U")

Standard Interpretation

Let us now estimate the circulating capital model with SI.

si1 <- clptheory::ppstdint1(
  A = ausdata$Ahat,
  l = ausdata$l,
  b = ausdata$b,
  Q = ausdata$Q,
  l_simple = ausdata$l_simple
)

New Interpretation

Let us now estimate the circulating capital model with NI.

ni1 <- clptheory::ppnewint1(
  A = ausdata$Ahat,
  l = ausdata$l,
  w = ausdata$wavg,
  v = ausdata$vlp,
  Q = ausdata$Q,
  l_simple = ausdata$l_simple
)

Let us see the uniform profit rate.

cbind(si1$urop,ni1$urop)
#>           [,1]     [,2]
#> [1,] 0.6018444 0.973433

Non-Regression-Based Measures of Deviation

Let us compute various non-regression-based measures of the deviation between the vector of relative labor values and the vector of relative prices of production for the SI.

nrsi1 <- clptheory::nregtestrel(
  x = si1$ppabs,
  y = si1$lvalues,
  w = ausdata$wagevector_all,
  w_avg = ausdata$wavg,
  mev = si1$mevg,
  Q = ausdata$Q
)

Let us do the same computation for the NI.

nrni1 <- clptheory::nregtestrel(
  x=ni1$ppabs,
  y=ni1$lvalues,
  w=ausdata$wagevector_all,
  w_avg=ausdata$wavg,
  mev=ni1$mevg,
  Q=ausdata$Q
  )

We can now compare the results for the analysis of the circulating capital model from the SI approach and the NI approach for the non-regression-based measures of deviation between relative prices of production and relative values.

comp1 <- cbind(nrsi1,nrni1)
colnames(comp1) <- c("SI","NI")
(comp1)
#>           SI        NI       
#> rmse      3.603886  0.6884111
#> mad       1.60151   0.4600684
#> mawd      0.713937  0.3040913
#> cdm       0.7897359 0.6472872
#> angle     63.92068  23.54431 
#> distangle 1.058664  0.4080406
#> lrelpplv  1128      1128

In the results above, we see the magnitudes of six different measures of the deviation between the vector of relative prices of production and the vector of relative labor values: root mean squared error (RMSE), meann absolute distance (MAD), mean absolute weighted distance (MAWD), classical distance measure (CDM), angle between the two vectors (angle in degrees), and distance computed using angle (distance).

As an example, we can see that the CDM for SI is 0.789 and for NI is 0.647. This can be interpreted as showing that the deviation between the vector of relative prices of production and the vector of relative labor values is 79 percent and 65 percent of the relative value vector according to the SI and NI methodology, respectively.

The last row of the above results shows the length of (number of observations in) the vector of relative prices of production or the vector of relative labor values. Recall that the input-output matrix is 48 by 48. Hence, the absolute value and price of production vectors will each be of size 48. Thus, the size of the vector of relative prices of production (or labor value) should be $(48 \times 47)/2=1128$.

Regression-Based Measures of Deviation

Let us compute various regression-based measures of the deviation between the vector of relative labor values and the vector of relative prices of production for the SI.

rsi1 <- clptheory::regtestrel(
  x = si1$ppabs,
  y = si1$lvalues
)

Let us do the same computation for the NI.

rni1 <- clptheory::regtestrel(
  x=ni1$ppabs,
  y=ni1$lvalues
  )

We can now compare the results for the analysis of the circulating capital model from the SI approach and the NI approach for the regression-based measures of deviation between relative prices of production and relative values.

comp2 <- cbind(rsi1,rni1)
colnames(comp2) <- c("SI","NI")
(comp2)
#>         SI          NI       
#> a0lg    -0.7787738  0.1341304
#> a1lg    -0.1450801  0.386964 
#> r2lg    0.001308835 0.1638283
#> fstatlg 143.914     550.9681 
#> pvallg  0           0        
#> nlg     1128        1128     
#> a0lv    1.736712    0.6057521
#> a1lv    -0.3923921  0.5908621
#> r2lv    0.002833572 0.22993  
#> fstatlv 35.7541     266.3688 
#> pvallv  0           0        
#> nlv     1128        1128

Regression-based tests of the deviation between use regressions, either log-log or level-level, of relative prices of production on relative labor value. The key the null (joint) hypothesis is that the intercept is 0 and the slope is 1.

The F-stat in the log-log regression of relative prices of production on relative value is 143.91 for SI and 550.97 for NI. In both cases, we can strongly reject the null hypothesis that the intercept is 0 and the slope is 1. The corresponding F-stats for the level-level regressions are 35.75 (SI) and 266.39 (NI). Once again, the null hypothesis is strongly rejected.

Example 2: Simple 3-Industry Set-up

This example was presented on pages 46-57 of E. M. Ochoa’s dissertation (Ochoa, E. M. 1984. Labor-Value and Prices of Production: An Interindustry Study of the U.S. Economy, 1947–1972. PhD thesis, New School for Social Research, New York, NY.). This example has also been discussed in Appendix B of Basu and Moraitis, 2023. (Basu, Deepankar and Moraitis, Athanasios, “Alternative Approaches to Labor Values and Prices of Production: Theory and Evidence” (2023). Economics Department Working Paper Series. 347. UMass Amherst. URL: https://scholarworks.umass.edu/econ_workingpaper/347/)

The Data

Let us load the library and create the data for our 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
)

# 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
l <- matrix(
  data = c(0.193, 3.562, 0.616),
  nrow=1
)

# Real wage bundle vector
b <- matrix(
  data = c(0.0109, 0.0275, 0.296),
  ncol=1
)

# Gross output vector
Q <- matrix(
  data = c(26530, 18168, 73840),
  ncol=1
)

# Market prices vector
m <- matrix(
  data = c(4, 60, 7),
  nrow=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 times
t <- diag(c(0.317, 0.099, 0.187))

# 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

Standard Interpretation

We will first implement the classical theory of prices for the circulating capital model and then turn to the capital stock model.

Circulating Capital Model

# Estimate circulating capital model with SI
si1 <- ppstdint1(
  A = A,
  l = l,
  b = b,
  Q = Q,
  l_simple = l
)

What is the uniform rate of profit?

si1$urop
#> [1] 0.3877843

What is the vector of labor values?

si1$lvalues
#>           [,1]     [,2]      [,3]
#> [1,] 0.4398417 7.739431 0.8979541

What is the vector of prices of production (absolute)?

si1$ppabs
#>           [,1]      [,2]     [,3]
#> [1,] 0.5703988 0.2388832 1.341621

Let us now compute the 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.

nrsi1 <- nregtestrel(
  x = si1$ppabs,
  y = si1$lvalues,
  w = w,
  w_avg = wavg[1,1],
  mev = si1$mevg,
  Q = Q
)

Capital Stock Model

# Estimate model
si2 <- ppstdint3(
  A = A,
  l = l,
  b = b,
  Q = Q,
  D = D,
  K = K,
  t = t,
  l_simple = l
)

What is the uniform rate of profti?

si2$urop
#> [1] 0.2337492

What is the vector of labor values?

si2$lvalues
#>           [,1]     [,2]      [,3]
#> [1,] 0.5192079 8.309406 0.9407729

What is the vector of prices of production?

si2$ppabs
#>          [,1]    [,2]     [,3]
#> [1,] 0.284253 1.66129 1.094453

Let us now compute the non-regression-based measures of deviation.

nrsi2 <- nregtestrel(
  x = si2$ppabs,
  y = si2$lvalues,
  w = w,
  w_avg = wavg[1,1],
  mev = si2$mevg,
  Q = Q
)

New Interpretation

We continue working with the 3-industry example and implement the New Interpretation of Marx’s labor theory of value.

Circulating Capital Model

# Estimate circulating capital model with NI
ni1 <- ppnewint1(
  A = A,
  l = l,
  w = wavg[1,1],
  v = v,
  Q = Q,
  l_simple = l
)

What is the uniform rate of profit?

ni1$urop
#> [1] 0.2116339

What is the vector of labor values?

ni1$lvalues
#>           [,1]     [,2]      [,3]
#> [1,] 0.4398417 7.739431 0.8979541

What is the vector of prices of production (absolute)?

ni1$ppabs
#>          [,1]     [,2]     [,3]
#> [1,] 2.621517 45.47507 4.703682

Let us now compute the 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.

nrni1 <- nregtestrel(
  x=ni1$ppabs,
  y=ni1$lvalues,
  w=w,
  w_avg=wavg[1,1],
  mev=ni1$mevg,
  Q=Q
  )

Capital Stock Model

ni2 <- ppnewint5(
  A = A,
  l = l,
  v = v,
  w = wavg[1,1],
  Q = Q,
  D = D,
  K = K,
  t = t,
  l_simple = l
)

What is the uniform rate of profit?

ni2$urop
#> [1] 0.1569311

What is the vector of labor values?

ni2$lvalues
#>           [,1]     [,2]      [,3]
#> [1,] 0.5192079 8.309406 0.9407729

What is the vector of prices of production (absolute)?

ni2$ppabs
#>         [,1]    [,2]     [,3]
#> [1,] 3.90503 48.3282 5.017568

Let us now compute the 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.

nrni2 <- nregtestrel(
  x=ni2$ppabs,
  y=ni2$lvalues,
  w=w,
  w_avg=wavg[1,1],
  mev=ni2$mevg,
  Q=Q
  )

Comparison of SI and NI

We can compare the results for the analysis of the circulating capital model from the SI approach and the NI approach for the non-regression-based measures of deviation between relative prices of production and relative values.

comp1 <- cbind(nrsi1,nrni1)
colnames(comp1) <- c("SI","NI")
(comp1)
#>           SI        NI        
#> rmse      23.68697  0.1064786 
#> mad       14.04216  0.09129555
#> mawd      1.51884   0.03132663
#> cdm       1.51884   0.03132663
#> angle     59.21479  3.519195  
#> distangle 0.9881081 0.06141188
#> lrelpplv  3         3

We can compare the results for the analysis of the capital stock model from the SI approach and the NI approach for the non-regression-based measures of deviation between relative prices of production and relative values.

comp2 <- cbind(nrsi2,nrni2)
colnames(comp2) <- c("SI","NI")
(comp2)
#>           SI        NI        
#> rmse      1.152957  0.295736  
#> mad       1.031963  0.2646106 
#> mawd      0.2125032 0.07588155
#> cdm       0.2125032 0.07588155
#> angle     51.23735  7.288633  
#> distangle 0.8647594 0.1271249 
#> lrelpplv  3         3

References

Basu, D. and Moraitis, T. (2023). Alternative Approaches to Labor Values and Prices of Production: Theory and Evidence. Economics Department Working Paper Series. 347. University of Massachusetts Amherst. Retrieved from https://scholarworks.umass.edu/econ_workingpaper/347/

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README.md

README.md

clptheory

Installation

Main Functions

Example 1: Analysis for Australia

Data

Standard Interpretation

New Interpretation

Non-Regression-Based Measures of Deviation

Regression-Based Measures of Deviation

Example 2: Simple 3-Industry Set-up

The Data

Standard Interpretation

Circulating Capital Model

Capital Stock Model

New Interpretation

Circulating Capital Model

Capital Stock Model

Comparison of SI and NI

References

Files

README.md

Latest commit

History

README.md

File metadata and controls

clptheory

Installation

Main Functions

Example 1: Analysis for Australia

Data

Standard Interpretation

New Interpretation

Non-Regression-Based Measures of Deviation

Regression-Based Measures of Deviation

Example 2: Simple 3-Industry Set-up

The Data

Standard Interpretation

Circulating Capital Model

Capital Stock Model

New Interpretation

Circulating Capital Model

Capital Stock Model

Comparison of SI and NI

References