The Soviet Price Determination

An Econometric Study

By   0. Kyn

I. Introduction

The purpose of this study is to estimate price equations for the econometric model of the Soviet economy. This implies two constraints on the general approach and methods used here:

1.The price model has to reflect the specific features of the Soviet price determination, and

2. it has to conform to the requirements and variables of the econometric model, it will be part of.

It is obvious that the whole mechanism of the Soviet price sett­ing is totally different from price mechanism in market economies. Prices have also much less essential role, because they do not directly influence choice of output, inputs and technology. Prices do not equilibrate supply and demand, especially not for producer goods, and they do not serve as criteria for allocation of scarce resources. Shortly, in the Soviet economic system the economic coordination is carried out primarily by direct quantitative tar­gets of the plan rather than by prices. Three specific features of the Soviet price system are particularly relevant here:

i. Most of the Soviet prices are set or approved by central authorities and they do not respond freely to the changing market conditions.

ii. As a result they remain constant or almost constant for quite a long time, but then are suddenly changed by a general price reform.

iii. The authorities set the prices on the cost plus basis, rather than according to supply and demand.

These three features must not be taken too literally. There is some although only small degree of decentralization in the Soviet price formation and even the central authorities do make some partial price adjustment in between price reforms. More importantly the Soviet firms do have limited possibility to influence prices especially by changing the structure of output and by develop­ing new products. As a result prices in the Soviet Union do change enough from year to year to make the price model meaningful. Disregarding the price changes would not be a crucial fault if the econometric model were to explain only the levels of output, if, however, profit and budget equations are to be incorporated in the model, explanation of price changes becomes indispensable.

It is quite clear that the price equation in the econometric model of the Soviet economy must be quite different than the price equations in the macro-econometric models of the market econo­mies. In the latter models prices are estimated mostly to get deflators of various macroeconomic aggregates. Inflation is not a serious problem for the Soviet economy and rather than concentrating on the changes in the price level it is more important to explain the changes in relative prices. Because the prices are set on the cost plus basis anyway, some kind of input-output cost plus price model will be appropriate. The size of such a mo­del and the actual variables entering in it must conform with the other parts of the econometric model.

In our case the econometric model contains five economic sectors:

1. industry,

2.agriculture,

3.construction,

4.transportation and communication

5.and the other (residual) economic sectors.

It will, therefore, be convenient to estimate the price equations just in this breakdown.

To estimate the cost plus price formulae the following information is needed:

-         input-output coefficients (for obtaining cost of material inputs)

-         wage rates and labor productivity (for obtaining wage costs)

-         capital per unit of output ratios (for estimating the capital costs).

Except for input output coefficients, which will be taken as exogenous, all the other necessary data will appear as endogenous variables of the econometric model.

II. Alternative price formulae

The cost plus pricing means, that the price of each commodity must include costs of material, wage costs and profit as a pro­portional surcharge on costs. Several alternative price formulae can be developed depending on the way profits are included into prices. Today quite an extensive literature on alternative price formulae exists. Most of this literature cones from the Soviet Union and Eastern Europe¹⁾, but it is closely related to works of Sraffa, Leontief, Morishima and others in the West²⁾. Without discussing the underlying theoretical justification we shall se­lect the few basic formulae, which according to our best knowledge correspond most closely to the pragmatic rules of price determin­ation in the Soviet Union. The following regressions should then help to determine, which one of the a priori selected formulae does explain the price formation in a given sector best’.

We shall use the following notation:

p_i …is the price of the i-th commodity (price index of the i-th sector)

a_ij…is the input-output coefficient representing the quanti­ty of the commodity i used as material input per unit of output of the commodity j

w…..is the wage rate in the production of commodity j

1…...is the quantity of labor input needed to produce one unit of the commodity j

k…...is the quantity of capital input needed to produce one unit of the commodity j in one unit of time

The most simple price formulae is the so called “labor-value price” which makes profits or “surplus value”, proportional to wage costs.

(1)      p_j      =       S_i  a_ijp_i + m_jw_jl_j             j = 1, 2, …., n        

According to the labor theory of value the coefficient m should be larger than one and the same in all sectors. There is no reason to expect the Soviet pragmatic price makers to follow ex­actly the labor theory of value. We shall, therefore, assume that m can be different in different sectors.

Next we shall formulate two types of the so called “two-channel prices”, i.e. prices which distribute profits simultaneously ac­cording to two principles. The first type of two-channel price makes one part of profit proportional to material costs and the other part of profit proportional to wage costs

(2)       p_j      =       a_j S_i a_ijp_i + m_j w_j1_j             j  = 1,2, .., n

Of course, both a_j  and m_j should be larger than one in this case.

The second type of the two-channel price makes one part of profit proportional to wage costs and the other part proportional to capital inputs needed per unit of output.

(3)         p_j      =       S_i  a_ijp_i + m_jw_jl_j  + r_j k_j            j  = 1,2, .., n

In this case m_j is to be larger than one and r_j should be nonnegative.

Finally we shall formulate the equation for the so called “three channel price” which is simply a combination of the two two-channel price types.

(4)     p_j      =       a_j S_i a_ijp_i + m_j w_j1_j + r_j k_j           j  = 1,2, .., n

The price formulae (1) to (4) as formulated here can be estimated without a problem, because we have all the necessary information for it. However, they deviate in few minor points from the ideal price types that were introduced in the above mentioned litera­ture.

One already mentioned difference is that we shall allow the co­efficients a_j , m_j and r_j to be different in different sectors. Secondly depreciation has not been introduced explicitly as cost in the price equation. This means, that depreciation - as well as other omitted costs - will have to appear as parts of the co­efficients a_j , m_j and r_j. Most logically depreciation should appear in r_j . Finally, the variable k_j in equations (3) and (4) should be properly multiplied by price index of capital goods. But neither of the five prices represents the price of capital goods and in addition to that it is not a Soviet practice to recalculate each year the value of capital stock at current prices so that keeping k_j at constant prices may be actually more rea­listic.

III.     Data

Most of the data for the estimation of price equations were taken from official statistical yearbooks of the Soviet Union, although some adjustment was needed)³⁾  The price indices (Table 1) for five sectors were calculated by taking the ratio of sect oral gross value of output in current and constant prices.

Table 1

Price Indices

            Industry       Agriculture     Construction   Transportation      Residual

  1958             99.740           108.950         107.980          69.110              104.210

  1959           101.400             98.770         105.510          72.460              107.690

  1960           101.420             98.990         108.870          75.630                99.820

  1961           101.890             97.860         108.220          75.260                96.560

  1962           101.400           110.210         106.070          73.160                99.780

  1963           101.400           118.330         108.460          72.760              103.860

  1964             98.520           116.390         108.280          72.720              104.580

  1965             97.910           126.790         108.110          74.090              102.010

  1966             97.490           131.150         106.430          72.020              102.520

  1967           102.030           130.860         114.150          73.980              101.590

  1968           106.430           134.470         112.760          71.470              103.770

  1969           106.190           140.800         120.970          69.470              108.620

  1970           106.180           150.870         111.090          70.810              109.600

  1971           104.210           155.090         122.660          72.860              112.720

  1972           103.880           163.360         116.570          73.090              119.820

  1973           102.950           156.900         114.650          72.180              119.950

This may not be truly correct price indices because the reported gross value of output in current prices is suspected to include underestimation of real price increases. Nevertheless even such price indices  show quite interesting changes in time. Prices in industry and transportation show some upward and downward movements, but overall relatively stable level. The main upward jump of industrial prices in the years 1966-1968 is clearly due to the general price reform. The increase of the price level due to the price reform is visible also in construction and the residual sector. Agricultural prices have been growing almost steadily and quite fast between the years 1961 and 1972.

The input-output coefficients were taken from the work of Vladimir Treml ⁴⁾ and revaluated at 1955 prices, i.e. base year prices of our price indices (see Table 3).

Table 3                 

Input-Output Coefficients*

at 1955 prices

                        1              2           3            4            5

1 Industry         .3816     .0983     .1447     .5158     .0815

2 Agriculture    .0979     .2115     .0002     .0006     .0030

3 Construct.      .0000     .0000     .0000     .0000     .0000

4 Transport.       .0839     .0202     .0028    .0017     .0109

5 Residual         .0426     .0442     .0000     .0130     .0149

* See TREML et al. (1972)

For lack of any further informa­tion about dynamic changes of input-output coefficients, we have assumed that the physical input-output coefficient has remained constant  during the whole observed period The changes in prices of material inputs caused a change in sectoral material costs (see Table 2) in spite of the constancy of input-output coefficients it is interesting to note, that the material costs are very high (50-60 percent) in industry and construction, somewhat smaller (20-30 percent) in transportation and agriculture and very small (l0 percent) in the residual sector.

Table 2

Material Costs

                 Industry     Agriculture  Construct.       Transport.      Residual

  1958         58.9668       38.8520      52.9793             14.6485          10.7623

  1959         59.1171       37.1043      53.8822             14.8997          10.9658

  1960         58.9929       36.8489      53.7937             14.9088          10.8748

  1961         58.8917       36.5045      53.9923             14.9756          10.8572

  1962         59.8746       39.1678      53.7852             14.9009          10.8798

  1963         60.2945       40.9245      53.1462             14.7059          10.8509

  1964         59.5480       40.3948      52.3652             14.4840          10.7305

  1965         60.3386       42.4482      52.0254             14.4015          10.6893

  1966         60.4531       43.3096      51.8145             14.3357          10.6534

  1967         62.2822       43.6932      54.1741             14.9981          11.0300

  1968         64.1970       44.9349      56.4428             15.6283          11.4045

  1969         64.7639       46.4238      56.3826             15.5890          11.4545

  1970         65.8999       48.6227      56.3982             15.5932          11.5136

  1971         65.8661       49.5008      55.4287             15.3147          11.4347

  1972         66.8715       51.5357      55.3562             15.2691          11.5410

  1973         65.8135       50.0655      54.8729             15.1308          11.4376

The low share of materia1 cost in prices of the residual sector results not only from the fact, that the residual sector contains such activities as for example trade and services, which actually need very little materia1 inputs, but also from the fact that practically all the turnover tax is concentrated in the output of the residual sector.

The sectoral wage costs (see Table 4) were calculated as a ratio of sectoral wage fund (i.e. the product of wage rates and the number of employees) to the sectoral gross value of out­put in constant prices.

In the same way as the price indices (Table 1) and the material costs (Table 2) the wage costs are expressed in percent of the base year (1955) prices. Table 4 reveals two opposite tendencies. The wage costs in industry and transportation has been declining - apparently due to the faster growth of labor productivity than average wages - while the wage costs in agriculture, construction and the residual sector were increasing.

The increase of wage costs in agriculture is quite remarkable, however, the increase of prices (Table 1) was almost proportional to it, so that the share of wage costs in prices has not changed much.

Finally Table 5 shows the sectoral capital-output ratios, that is the ratios of the stock of fixed capital to the gross value of output - both in constant prices. Again we see quite large differences in levels as well as tendencies of capital-output ratios.

IV. Regression Results

On the first glance the price equations are a typical example of nonrecursive simultaneous model. The closer look will, how­ever, reveal that the equation (1) and (3) would not actually suffer by a direct simultaneity bias, because for the purpose of estimation material costs will be transferred to the left hand side of the equation. There may still remain some simultaneity problems if we think of price equations as a part of the whole econometric model, because then the wage rates and the sectoral labor-output and capital-output ratios may be dependent on prices, however no simultaneity will appear directly inside the price subsystem.

The equations (2) and (4) are clearly simultaneous and should be, therefore, estimated by two-stage or three-stage least squares or ­some other similar method. In this paper only OLS and CORC (Cochran­-Orcutt) estimates will be reported. The two and three stage least squares estimations will be postponed after the specification of the other parts of the econometric model is completed.

Table 6 brings estimates of the labor-value prices. The results are interesting, but we do not expect, this type of prices to ex­plain the Soviet price formation particularly well. The high t­-statistics are not really surprising, because it is the only estimated coefficient in the regressions.

Table 6

Estimates of Labor-value Prices

1958 - 1973 

Eq. (1)

 Remarks: t-statistics in parenthesis

DW is the Durbin-Watson statistic

SER is the standard error of regression

ARC is the first order autoregressive coefficient                                                 

R² is not really meaningful in these regressions without constant terms. They are reported only when the sum of residuals is close to zero.

Except for transportation the fit seems to be quite good but the autocorrelation is very high. It is interesting that only three distinct values of, m were found among five sectors. In­dustry and agriculture have relatively high, m around 2.7 while construction and transportation have somewhat smal1er m around 2.2 . The extremely high m = 6 in the residual sector can be ex­plained by the fact, that practically all the turnover tax is concentrated in prices of the residual sector.

Table 7 brings estimates of two channel prices, which distributes part of the profit proportionate1y to material costs and part proportionately to wage costs. The new estimated parameter a ­turned out to be always larger than one and statistically signi­ficant, while the parameter b lost considerably on its value and significance. Especially in agricu1ture, transportation and the residual sector prices seem to be set more on the basis of material cost than wage costs. On the other hand industry and construction show a moderate surcharge of 20-30 per cent on ma­terial costs and a larger surcharge of 50-100 per cent on wage costs.

Table 7

Estimates of Two-Channel Prices

                   1958 - 1973                 

Eq. (2)

We must not forget, however, that both; the OLSQ and CORC esti­mates of the equation (2) may be biased. The disadvantage of both types of prices estimated so far, was that the models did not allow for an effect of the price reform of 1967. The price reform had two effects: it increased the level and changed the type of prices by introducing the “capital charge”, i.e. the tax on capital assets. One possible way of capturing the effect of the price reform in our model would be to assume that the price determination before the reform was based on the labor value formula and that in the reform capital charge was just added to prices. This leads to a modified equation (3)

(3a)        p_j      =       S_i  a_ijp_i + m_jw_jl_j  + r_j k_j d      j  = 1,2, .., n

where the dummy variable d is determined in the following way

d = 0 for the years 1958-1966

d = .5 for 1967      (to capture the partial effect of the reform in the first year)

d = 1 for the years 1968—1973.

Formula (3a) gave good results only for industry, agriculture and transportation (see Table 8). The estimated r’s were negat­ive in construction and the residual sector and, therefore, the regressions for these two sectors are not reported.

Table 8

Estimates of Two-Channel Prices

1958 — 1973

  Eq. (3a)

with the effect of price reform

The results of Table 8 are not fully satisfying. The autocorre­lation is still high and the capital charge in industry and transportation seems to be too low  (2.5 - 4 per cent). The model ( 3a) is, however, definitely an improvement over the simple la­bor-value price as can be seen from the comparison of the actual and  fitted values in Tables 9a and 9b.

Table 9a

A Comparison of Actual and Fitted Values

Equations (1) and (3a)

The compared variable in this case is value added, i.e. price minus material costs

Table 9b

 A Comparison of Actual and Fitted Values

(continuation of Table 9a)

Equation (1) and(3a)

An alternative way of modeling the impact of price reform is to  assume that the ‘capital charge” was added to the two-channel prices of the type (2). This leads to the modified three-channel formula

(4)          p_j      =       a_j S_i a_ijp_i + m_j w_j1_j + r_j k_j d           j  = 1,2, .., n

where d is the same dummy variable as in the equation (3a).

The estimates of the equation (4a) are shown in the Table l0.

Table 10

Estimates of Three-Channel Prices

1958 — 1973

  Eq. (4a)

with the effect of price reform

Again only three out of five sectors gave economically meaning­ful result, but two of them, namely industry and agriculture, are not really preferable to the results obtained from the model (3a).

Although the results of Table 10 are not fully satisfactory, one can still regard the model (4a) as an improvement over the simple two-channel price (2) which disregards the effect of price reform. These is best seen from Tables 11a and 11b which compare the fitted values of these two models.

Table 11 a

A Comparison of Actual and Fitted Values

Equation (2) and (4a)

Table 11 b

A Comparison of Actual and Fitted Values

(continuation of Table 11a)

Equation (2) and (4a)

V.      Conclusions

In this paper an attempt has been made to estimate the model of the Soviet price determination. This model, which consisted of price equations for five sectors of the Soviet economy, is intended to be a part of a larger econometric model of the Soviet economy. Four different cost-plus price formulae were estimated. First two formulae disregarded the price reform and distributed the profits either proportionally to wage costs (labor value prices) or proportionately to both wages and material costs (two channel prices). The other two formulae were modifications of the previous two. They included a “capital charge” into prices the post reform years. Considering the shortness of time series relatively poor quality of data and the fact, that the Soviet centralized price determination is generally regarded to be quite arbitrary, almost all the regressions gave surprisingly good results. The second pair of formulae, which included the assumed effect of the price reform gave recognizably better results than the first pair except for the residual sector. Considering both the statistical properties and economic meaning of estimates, it is possible to select the type (3a) as best for industry, agriculture and transportation and the type (4a) as best for con­struction, The price equation for the residual sector will either have to be re-estimated or the simple labor-value price must be taken as the best result.

Although this exercise demonstrated that one can get statistically good and economically meaningful results by estimating cost-plus price equations for the Soviet economy the work on the price submodel cannot be regarded as satisfactorily finished. The persistent presence of autocorrelation even in the best results indicates that some alternative specifications of the price model - possibly including time lags - should be examined. The attempt must be also made in future to eliminate the simultaneity bias and possible contemporaneous correlation by using Zellner’s and/or three stage least squares estimators.

References

 BELKIN, V.D.: Tseny yedinnogo urovnya i ekonomicheskiye izmereniya na ikh osnove (Moscow, 1963)

DMITRIYEV, V.K. Ekonomicheskiye ocherki (Moscow 1904)

KYN, 0., SEKERKA, B., HEJL, L. A Model for the Planning of Prices, in:Socialism, Capitalism and Economic Growth. Cambridge University Press, 1967.

LEONTIEF, W.: The structure of the American economy, 1919-1929; An empirical application of equilibrium analysis. Cambridge Massachusetts: Harvard University Press, 1941.

MORISHIMA, M. and SETON, F. Aggregation in Leontief Matrices and the Labour Theory of Value, Econometrica, April 1961, 29, S. 203—20.

NEMCHINOV, V.S. Osnovnye kontury modeli planovogo tsenoobrazovaniya, Voprosy okonomiki, 12/1963.

SCHRETTL, W.: Indices versus Absolutwerte in der sowjetischen Kapitaistockstatistik, Arbeiten aus dem Osteuropa-Institut Munchen (Working Papers) N0. 17, Munich, March 1976.

SRAFFA, P.    Production of commodities by means of commodities. Cambridge University Press, 1960.

TREML, V.G., GALLIK, DON._, KOSTINSKY, B.L., and KRUGER, K.W.

The Structure of the Soviet Economy. Analysis and Reconstruction of the 1966 Input-output Table, New York (Praeger) 1972.

VINCENTZ, V.  Zur Konstruktion von Zeitreihers für die sowjetische Wirtschaft: Sektorale Produktions und Arbeitskrafte­daten, Arbeiten aus den Osteuropa-Institut Munchen (Working Papers) No.16, Munich, Dec.1975.

FOOTNOTES

1)    See for example DMITRIYEV(l904), BELKIN(1963), NEMCINOV (1963), KYN, SEKERKA, HEJL (1967) (back)

2)    See SRAFFA (1960), LEONTIEF (1941), MORISHIMA (1961)  (back)
3)    For more detailed description of data and of adjustments made see SCHRETTL (1976), VINCENTZ (1975) (back)
4)  See TREML at al. (1972)  (back)