Optimal Technological Choices After a Structural Break:The Case of the Former Communist Economies

Hernan Moscoso BoedoCarl H. Lindner College of Business

University of Cincinnati

September 6, 2018

Abstract

This paper analyzes the transition observed after the fall of communism in EasternEurope and the former Soviet Union. It uses a general equilibrium model where theskill bias in the production technology is optimally chosen. As observed in the data, themodel produces significant temporary losses in output and physical capital together withincreases in the skill premium, suggesting that part of the transition can be explainedby a costly adjustment process to new technologies.

Keywords: Endogenous Skill Biased Technical Change, Transition EconomiesJEL Classifications: E25, J24, O33, O57, P27

1 Introduction

The collapse of communism in the early 1990s initiated a set of transformations that continue

to take place in Eastern Europe and Asia. After the communist regimes fell, a transition to

a market economy took place, with patterns that repeated themselves in almost all of the

former centrally planned economies. Among the most notable effects of this transition were

a U-shape behavior in terms of GDP per capita and capital stocks, together with increases in

the returns to education and inequality. There were also profound changes to the production

structure of the economy, with a dramatic decrease in the public sector participation as well

as changes in the sectoral composition of the economy.

1

This paper explains the initial transition period as the result of the costly adoption of new

optimally chosen technologies. In the model proposed here, it is the behavior of the endoge-

nous skill bias that determines the transitional dynamics observed during the 1990s. The

salient characteristics of the former communist economies regarding the interaction between

production, education and skills were basically three. First, the fraction of skilled labor force

in the centrally planned economies was comparable to the levels observed in the developed

economies of the west. Second, the production structure showed an inherent unskilled bias

when compared to other more developed economies. That is, while having a highly educated

labor force, the sectoral structure of production was similar to that of a developing coun-

try, with manufacturing shares that doubled the shares observed in the developed world as

well as a very large public sector. These two factors imply a third fact, which was a very

low return to education during communism as shown by Fleisher, Sabirianova and Wang

(2005) and Gorodnichenko and Sabirianova Peter (2005). Close to the idea of a costly tech-

nological transition presented in the model, Sabirianova (2002) also documents the human

capital reallocation process in transitional Russia, and finds that workers that suffer negative

shocks transition to occupations with lower human capital requirements. Suggesting that the

transition might have affected existing stocks of human capital.

The theoretical model is calibrated as much as possible to data from the former communist

economies, where the initial technology is assumed to be exogenous, and then model the

transition out of communism as the dynamics of optimally determined skill bias parameters

in production. The model is in line with the data in terms of output, inputs (human and

physical capital), as well as prices (the returns to education).

Milanovic (1998) studies the evolution of various indicators in the post communist tran-

sition, focusing on income, poverty and inequality. When referring to the evolution of out-

put argues that “After the Great Depression of 1929-33, this decline represents the largest

peacetime contraction of world output”. In terms of income distribution Milanovic (1998)

documents increases in the Gini coefficient in every country involved, with an average of 9

2

points, from 24 to 33 in a very short period of time. Closer to the nature of the model Gorod-

nichenko and Sabirinova Peter (2005) report large increases in the returns to education in

Russia (from 4% to 9%) and more modest ones in the Ukraine, suggesting that the dynamics

of transition were somewhat heterogeneous among these countries.

The endogenous technological transition is at the core of the dynamics generated in this

paper. This is meant as complimentary to other sources of well known variation during the

transition. As such, it is only partial and should not be expected that the model explains all

the features observed in the data. The model abstracts from other issues that are of first order

of importance. Some of the critical factors in the Russian transition are explained by Shleifer

and Treisman (2005), where they explore the implications of political instability, increases in

inequality, corruption and financial volatility. Other factors should also be mentioned, such

as the increase in unemployment, brain drain,1 and even war. There is no doubt that some

of these aspects played a key role in the loss of output and increases in inequality observed

after the fall of communism.2

The paper is organized as follows: Section 2 presents the model economy, where the choice

of production technology is at the center of the economic problem. Section 3 calibrates the

model to the former soviet states. Section 4 analyzes the dynamics of the economic aggregates

in the event of a sudden regime change, and finally section 5 concludes.

2 The Model Economy

The basics for the model were developed in Moscoso Boedo (2010). The key feature of the

model is that the skill bias in the production function (a nested CES with skilled labor,

unskilled labor and physical capital) is endogenous. The optimal skill bias is a function of

total factor productivity as well as the stocks of skilled workers and physical capital. The

1The effects of the brain drain were shown by Suzuki (2018) for the case of Serbia.2It is not the objective of the paper to fully explain all the features of the data, but to provide a simple

model where some of the features observed in these economies can be rationalized.

3

main assumption affecting the transition dynamics is that changes in the skill bias parameter

are not free. There is a convex cost in terms of inputs (skilled workers and physical capital)

anytime the planner chooses to change the parameters in the production function.

The utility function of the infinitely lived representative consumer is given by

∞∑t=0

βtu (Ct) (1)

The planner in this economy maximizes (1), subject to the following budget constraint

Ct + It ≤ F (bt, Kpt , Spt , Upt) (2)

where Ct denotes consumption in period t, It denotes investment in physical capital in

period t, and F (.) denotes the production function of final goods. F (.) is a function of the

following arguments: bt indexes the technology adopted in period t (or its skill bias), that

is, there will be a continuum of functions F (bt, .) indexed by bt from 0 to 1, and in period t

the actual production function adopted will be the one indexed by bt. Once the production

function is determined by bt the amount produced is a function of the physical capital, the

skilled labor and the unskilled labor devoted to the production of final goods, Kpt , Spt , and

Upt respectively.

The technology adjustment cost function G (bt, bt+1) maps changes in the skill bias in

production to adjustment costs, with the following properties: G(bt, bt) = 0 and G(bt, bt+1) >

0 for bt 6= bt+1. These adjustment costs can be interpreted as accelerated depreciation of

the stocks of physical capital and skilled labor or obsolescence due to technological change

of those stocks. This idea of an adoption cost can be traced to the existing literature,

where skills are technology specific, as in Chari and Hopenhayn (1991), or that technology

is embedded in physical capital as in Jovanovic (1998). Those are extreme cases of a cost

function where physical and human capital are technology specific. For example, In the case

4

of the former communist countries, skills related to the public administration of production

resources become unnecessary once the market forces are allowed to determine the allocation

of resources. Also, physical capital devoted to the production of antiquated automobiles

in Eastern Germany, lose their productive use and become obsolete. So this technology

adjustment cost function can be thought of as capturing an average cost of transition from

one technology to another.

In the particular case of the former communist economies, there are two salient transitions

that could have generated an accelerated depreciation of the stocks of physical and human

capital. First, the decrease in the public sector share of the economy and the sectoral shift out

of manufacturing and into services. The transition into services is a fact for all the economies

Eastern Europe, as shown in Bah and Brada (2009). More directly related to the accelerated

depreciation mechanism proposed in the model, Sabirianova (2002) documents the human

capital reallocation process during the Russian transition to a market economy and finds

that workers that suffer negative shocks transition to occupations with lower human capital

requirements.

From a methodological perspective, Piazolo (2001) advocates for the inclusion of adjust-

ment costs that depend on the change on the observed parameter. He argues that such

formulation of the adjustment cost leads to behaviors that mirror the empirical data in the

first years of the transition, which is similar to what the function G(bt, bt−1) does in the

context of the model.

The stocks of skilled labor, unskilled labor and physical capital, are divided as follows:

Upt + Uet + Spt + Set ≤ 1 (3)

Kpt +Ket ≤ Kt (4)

5

Upt ≥ 0, Uet ≥ 0, Spt ≥ 0, Set ≥ 0 (5)

Where a variable with a subscript p denotes that that variable is being used in the pro-

duction of final goods, and a variable with an e subscript denotes a variable that is being

used in the production of skilled workers (interpreted as the educational sector). Variables

without p or e subscript denote aggregates of physical capital or skilled labor.

The production of skilled labor is given by a function H (Ket , Set , Uet). Where I interpret

the function H (Ket , Set , Uet) as the output of the educational sector. Therefore Setdenotes

the skilled workers in the educational sector, or teachers, Uet denotes the students and Ket

the physical capital in the educational sector.

The law of motion for the stocks of physical capital and skilled workers are as follows:

St+1 ≤ St [1− δs −G (bt, bt+1)] +H (Ket , Set , Uet) (6)

Kt+1 ≤ Kt [1− δk −G (bt, bt+1)] + It (7)

Combining (2) and (7) we get

Ct +Kt+1 ≤ F (bt, Kpt , Spt , Upt) +Kt [1− δk −G (bt, bt+1)] (8)

So, the problem can be written as, maximize (1), subject to (3), (4), (5), (6), and (8)

Note that the accelerated obsolescence of physical capital renders it useless, while it shifts

human capital from skilled to unskilled. There is a parallel interpretation between these two

effects which is that both investments (in physical capital and human capital) become useless

after the technological transition. One way to think about it is that there is a fraction of

these investments (in terms of capital or skills) that are technology specific and are lost when

that particular technology is not used anymore.

6

2.1 Functional forms

The model stated above requires the choice of functional forms for the functions u(), F (),

G(), and H().

The instantaneous utility function is assumed to be of the following form:

u (Ct) =C

(1−ϕ)t

1− ϕ

The technology adjustment cost function G() is given by

G (bt, bt+1) = eζ(bt+1bt−1

)2

− 1 (9)

This function satisfies the requirements stated above, G(bt, bt) = 0 and

G(bt, bt+1) > 0 for bt 6= bt+1.

Note that the function G (bt, bt+1) is convex, which is in line with the literature of convex

adjustment costs, which induce the planner (or the market) to take small steps in adjusting

the technology instead of making big jumps. Also note that the function G (bt, bt+1) has the

property that its derivatives in steady state are equal to zero. The function G (bt, bt+1) is

affected by only one parameter, ζ. As ζ increases the costs associated with technological

change (in terms of skilled workers and physical capital), increase, affecting the dynamic

transition of the model (while not in steady state).

The production function of final goods, F (.), follows the functional form of choice in Funk

and Vogel (2004), and is calibrated to moments estimated by Krusell et. al. (2000). This

functional form (together with its calibrated parameters) has the characteristic of inducing

skill biased technical change as a result of total factor productivity improvements.

The production function used in the quantitative exercise is given by

F (bt, Kpt , Spt , Upt) = zt

{bt[aUρ1

pt + (1− a)Kρ1pt

] ρ2ρ1 + (1− bt)Sρ2pt

} 1ρ2 (10)

7

Finally the function H() is assumed to be Cobb-Douglas:

H (Uet , Set , Ket) = ψUµetS

ξetK

1−µ−ξet (11)

3 Calibration

The model is calibrated to moments obtained for the Soviet Union in the communist era and

for The Russian Federation afterwards. Given data availability issues, some parameters are

chosen to match US moments as well. The calibration exercise for the former communist

countries adds an additional level of complexity given by the choices at the start of the

transition period. Parameters are calibrated to match moments 20 years after the transition

began (around the year 2010), and the initial conditions are taken from the data as much as

possible.

Given the high levels of education in the former communist economies, the definition of

skills is that of tertiary education. We assume that individuals are born with secondary

education (or exogenously mandated to complete secondary education) and then choose to

invest in human capital to become skilled. The investment in human capital is assumed to

be for 6 years. In other words we assume that a skilled individual with tertiary education

ends up investing for a total of 16 years, and starts his/her decision making process when

they have 10 years of education, which is exogenously given.

The technological transition cost ζ is set to zero in the baseline calibration and then

changed to explore its effects on the aggregates.

The model is calibrated so that it delivers 55% of its labor force as skilled. This statistic

was obtained from OECD (2012). Specifically 55% of the Russian Federation’s labor force

between the ages of 25 and 34 attained tertiary education by 2002. The relatively limited

age group used to calibrate the final steady state is intended to clean the effects from older

generations educated under the previous regime, that would drive the fraction of skilled

8

downward. Other statistics are in line with this observation. Lee and Lee (2016) report that

56% or the Russian Federation’s labor force had some tertiary education in 2005.

The second parameter calibrated to Russia, is the total factor productivity. In the nu-

merical exercise, TFP is fixed, and the dynamics will be generated solely by technological

transitions related to the skill bias parameter. z is set to match the relative to the US Russian

GDP per capita from to Feenstra et. al. (2015), which was around 30%.

Finally the returns to education or (skill premium) are calibrated to the later numbers

given in Gorodnichenko and Sabirianova Peter (2005) for Russia. The returns to education

are estimated to be 9.2% per year of investment in education.

The rest of the parameters, are set to match the consumption-output ratio for the Russian

Federation from Feenstra et. al. (2015) for the year 2014 at 76% and the capital share at

34.3%. Note that these last two moments are later in the transition so as to be closer to a

concept of steady state.

The parameter values presented in table 1, are set so as to match as close as possible the

moments presented in table 2.

The parameter values are:

Table 1: Parameter values in the model

Parameter z ψ µ a ρ1 ρ2 ξ δs δk β ϕ ζ

Value .52 .2 .75 .5 .75 −.2 .176 .02 .08 .96 2 0

Which match the following moments around 2010.

9

Table 2: Identifying moments.

Comparison between the model and the data

Moment Model Data

Skill Premium 1.68 1.74

Skilled workers .55 .55

Consumption Output Ratio .76 .78

Students over Labor Force .09 .076

Expenditure per pupil over GDP per worker .14 .163

Capital Share of GDP .336 .343

Wage expenditure in education .7036 .7036

σS,UσS,K

2.62 2.49

The return to 6 years of schooling calculated as exp(ωt6), where ωt equals the return to

one year of high school for Russia reported in Gorodnichenko and Sabirianova Peter (2005)

for the year 2000. Skilled workers are obtained from From OECD (2012). The consumption

output ratio is the ratio of Consumption to output reported by Feenstra et. al. (2015) for

Russia for the year 2012. The ratio of students over labor force is calculated as the ratio of

students enrolled in tertiary school to labor force (obtained from ILOSTAT (2017) and the

UNESCO (2018) educational snapshot of the Russian Federation). Expenditure per pupil

over GDP per worker was obtained from Feenstra et. al. (2015) and OECD (2012). The

capital share of GDP was obtained from Feenstra et. al. (2015) for the year 2014. Finally,

two moments are calibrated to US levels given data availability. First σS,U equals the partial

elasticity of substitution between S and U. Therefore,σS,UσS,K

is the ratio of partial elasticities

of substitution between S and U and S and K. According to Krusell et al (2000) it is 2.49,

which is based in turn in calculations reported by Hamermesh (1993). Second, the wage

expenditure in education is calibrated to match educational wages over total educational

expenditures from the Statistical Abstract of the US.

10

3.1 Initial Conditions

In order to analyze the collapse of the communist regime, one must define what the former

regime means in terms of the model. In particular, the initial conditions have to mirror

observables (such as the stock of skilled workers, physical capital, and output), as well as

model-defined variables such as the skill biased parameter b. Three different explanations

all point towards a relatively unskilled bias production technology during the communist

regimes.

First, the relatively unskilled bias in production during the communist era is suggested by

the behavior of the skill/technology related variables over time and around the transition in

particular. In this regard two features of the data point towards unskilled bias in production

at the end of the communist regime. First, there was a dramatic increase in the returns to

education right after the transition together with a stock of skilled workers that was on par

with the developed nations before the collapse of the communist regimes. In other words,

before the collapse, the centrally planned economies displayed high levels of human capital

with low returns to education, leading us to believe that the skill bias in production was low (or

that the stock of skilled workers was higher than expected from its total factor productivity).

The second data related observation comes from international comparisons. Looking at the

US as a benchmark, it has been pointed out that the increases in inequality generated by the

skill bias technical change process, had a correlations with changes in production structure

of the economy. In particular, the manufacturing sector suffered a decrease in its labor

share of almost 50% in the US as Figure 1 shows. Taking the US experience, and using the

manufacturing sector share of the labor force as a proxy for the unskilled bias in production,

it can be seen that the Soviet Union at the end of the 1990s was similar to the US in the mid

1950s, where the skill bias in production was much lower.

11

Figure 1: Evolution of the Labor Force share in Manufacturing

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990

0.2

0.25

0.3

0.35

0.4

Year

Labor

Forc

e s

hare

in M

anufa

ctu

ring

Soviet Union

USA

Note: The labor force share in manufacturing for the Soviet Union obtained from the SlavicResearch Center Soviet Database. The labor force share in manufacturing for the US wasobtained from the Federal Reserve Economic Data FRED.

The second reasoning behind the idea that the production technology was relatively un-

skilled biased in the Soviet Union before its collapse has to do with the theoretical behavior

of a similar model in Moscoso Boedo (2010). In that paper, the US undergoes a major transi-

tion towards skilled biased technologies as a consequence of exogenous improvements in total

factor productivity. Putting together the data and the predictions of the model presented in

Moscoso Boedo (2010), the skill biased parameter in the mid 1950s for the US was roughly

30% lower (meaning that it was that much more biased towards the unskilled labor input).

Finally, given the obvious income redistribution characteristics of the former communist

regimes, one alternative would be to incorporate a government into the model and solve for

12

the decentralized equilibrium3, where this government taxed close to 100% of income and

transferred on a per capita basis, across workers. Under that approach, the optimally chosen

skill bias parameter at taxation level close to 100% is around 0.6, which is endogenously

relatively unskilled biased compared to cases where taxes are lower. A simpler, but analogous

way to proceed is, to set that technology parameter around 0.6 and derive a steady state where

the technology parameter is not a choice anymore. Then, the transition from a centrally

planned to a market economy is modeled as an expansion of the set of available technologies

(going from a skill bias parameter to a skill bias endogenous variable).4

All these observations lead us to believe that the production technology at the end of

the communist era was relatively unskilled biased by factors between 25% and 50%. In

the experiment we will analyze the case where the skill bias in technology is 25% more

unskilled biased before the break as a conservative view of the transition. While the parameter

determining the skill bias in technology can be though of as coming from the demand side,

we also have skilled labor supply side statistics, and will start the economy with a stock of

skilled workers given by the data at 55% of labor force.

This particular way of modeling the transition abstracts from the effects of changes in total

factor productivity that could have occurred during the 1990s and beyond. The experiment

consist only on allowing the economy to converge to its long term equilibrium given that it

starts off that equilibrium in terms of skill bias and the stock of skilled workers.

4 Dynamics

The experiment consists on starting the economy on an initial point that captures the salient

features of the communist regime at the end of the 1980s. In particular, we start the economy

with the observed fraction of skilled labor force at 55%, a technology parameter fixed at 25%

3See the appendix for a description of the decentralized equilibrium.4Alternatively, the regime change can be interpreted as a change in the technology change parameter ζ

from ∞ to some finite value.

13

above its steady state when b is a choice variable, and a stock of physical capital in steady

state given its total factor productivity parameter, and allow the economy to transition to its

new steady state equilibrium. Note that TFP is assumed constant throughout the exercise.

Thus, it is possible to view this experiment as tracking the dynamics of the economy to a

one time change in the cost of adjusting technologies, ζ, which we assume took place around

1990.

From now on the dynamics of the system are analyzed. In particular, the following

variables are of interest: the evolution of the skill bias parameter given by (1− b), the stock

of physical capital, the stock of human capital (measured as the fraction of skilled workers),

total output and the evolution of the skill premium. All the variables are to be followed for

different values of the parameter determining the technological transition cost ζ. ζ will take

values from zero up to 30. In essence, the experiment will be conducted for different values

of the endogenous depreciation process related to technological change.

First, figure 2 shows the evolution of the skill bias parameter as a function of the cost of

technical change given by ζ.

14

Figure 2: Evolution of the skill bias parameter (1− b)

0 2 4 6 8 10 12 14 16 18 200.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Period

(1−

b)

ζ=0

ζ=0.05

ζ=0.5

ζ=1

ζ=10

ζ=20

ζ=30

Note: Evolution of the model generated skill bias parameter expressed as (1 − b). Highervalues represent a relatively skilled biased technology. The series is shown for different val-ues parameter ζ in the technology adjustment cost function G(bt, bt+1). Higher values of ζrepresent higher adjustment costs.

Two salient features are to be observed in this figure. First, the skill bias in production

increases over time. That is almost by construction by the fact that the initial conditions

were assumed to be such that the original technology was relatively unskilled biased and the

initial stock of skilled workers was higher that the steady state of the model. Both forces are

leading the planner to increase the productivity of the skilled labor force. Second, given the

shape of the technical transition cost, the higher the cost, the slower the transition. Under the

convex cost, the economy slowly changes technology as the costs increase so as not to destroy

too many inputs through the endogenous accelerated depreciation induced by changes in b.

15

Figure 3 shows the evolution of the stock of physical capital. It is almost a mirror image

to the evolution of the skill premium. The faster the skill premium changes, the faster the

stock of capital falls allowing for a faster transition. As in the data, the stock of capital falls.

In the model it falls because the planner shifts towards skill intensive technologies, and by

doing that, lowers the relative productivity of the unskilled labor force and physical capital

(which are assumed to be complements).

Figure 3: Evolution of the capital stock

0 2 4 6 8 10 12 14 16 18 200.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Period

K

ζ=0

ζ=0.05

ζ=0.5

ζ=1

ζ=10

ζ=20

ζ=30

Note: Evolution of the model generated physical capital stock. The series is shown fordifferent values parameter ζ in the technology adjustment cost function G(bt, bt+1). Highervalues of ζ represent higher adjustment costs.

In the data, the evolution of the capital stock for the Russian Federation (obtained from

Feenstra et. al. (2015)), had a dramatic behavior as shown in figure 4

16

Figure 4: Evolution of the capital stock in the data

1990 1995 2000 2005 2010 20150.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Year

Capital S

tock

Note: Data from Feenstra et. al. (2015) for the Russian Federation. Capital stock at currentPPPs relative to initial year (1990).

The capital stock decreases by almost 50% in 12 years after the transition started. The

speed at which the capital stock was lost, is only matched halfway by the model for the cases

of technological transition costs in the order of ζ = 0.5 to ζ = 1, generating almost 30%

losses at the 12 to 15 year mark. Also note a slow recovery in the later part of the period

generated at those levels of adjustment costs. Note that the in the model there are no changes

to the total factor productivity parameter z, which, if increasing, could also be generating

endogenous increases in the level of capital.

The other key production input is given by the fraction of skilled labor force. Figure 5

shows the model generated evolution of the stock of skilled workers over time as a function

17

of the technological transition cost.

Figure 5: Evolution of the skilled labor force

0 2 4 6 8 10 12 14 16 18 200.52

0.54

0.56

0.58

0.6

0.62

0.64

0.66

0.68

0.7

Period

S

ζ=0

ζ=0.05

ζ=0.5

ζ=1

ζ=10

ζ=20

ζ=30

Note: Evolution of the model generated stock of skilled workers. The series is shown fordifferent values parameter ζ in the technology adjustment cost function G(bt, bt+1). Highervalues of ζ represent higher adjustment costs.

In this case, under all specifications of the adjustment cost ζ the stocks of skilled workers

increase, even after having started above the long term equilibrium levels for the skill bias

parameter in production. The skill bias parameter converges to a value where the productivity

of the skilled workers increases and therefore the planner increases the stock of skilled workers,

at the expense of unskilled workers and physical capital. Notice that the increase in the stock

of skilled workers is between 15% and 20%.

18

Figure 6: Evolution of the skilled labor force in the Russian Federation

1985 1990 1995 2000 2005 201025

30

35

40

45

50

55

60

65

Year

Skill

ed P

opula

tion

Note: Fraction of the population between ages 15 to 64 with tertiary education. Source: Leeand Lee (2016)

While not as dramatic as in the data, the model captures a large fraction of the increase

in the stock of educated workers after the transition out of communism.

The evolution of inputs together with that of technology determines the evolution of

output per person. Figure 7 shows the model generated evolution of output as a function of

the technological adjustment cost.

19

Figure 7: Evolution of output per worker

0 2 4 6 8 10 12 14 16 18 200.8

0.85

0.9

0.95

1

1.05

Period

Outp

ut per

work

er

ζ=0

ζ=0.05

ζ=0.5

ζ=1

ζ=10

ζ=20

ζ=30

Note: Evolution of the model generated output per worker. The series is shown for differentvalues parameter ζ in the technology adjustment cost function G(bt, bt+1). Higher values ofζ represent higher adjustment costs.

Figure 8 shows the evolution of the Russian Federation’s output per worker after the

collapse of communism.

20

Figure 8: Evolution of output per worker in the data

1990 1995 2000 2005 2010 20150.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Year

Outp

ut per

work

er

Note: Data from Feenstra et. al. (2015) for the Russian Federation. The series of output perworker constructed as rgdpo/emp in the database.

The model is able to capture roughly 40% of the drop in output observed in the data at the

higher end of the transition cost parameter. The U-shape behavior in output observed in the

data and generated by the model for most of the technological transition cost parameter can

now be analyzed with the help of the model. The initial drop in output is generated by the

endogenous move towards skill biased production technologies. The endogenous movement

towards relatively skill biased production technologies accelerates the depreciation of both

physical and human capital, destroying inputs and lowering output. The increasing phase

of the U-shape in the latter years has to do with a reversal process. The economy not only

transitions towards skill biased production, but also invests in physical and human capital

21

that is now more productive given the new technology.

Finally, figure 9 shows the model generated evolution of the skill premium as the ratio of

the wages of skilled workers to unskilled workers.

Figure 9: Evolution of the skill premium

0 2 4 6 8 10 12 14 16 18 200.8

1

1.2

1.4

1.6

1.8

2

2.2

Period

Skill P

rem

ium

ζ=0

ζ=0.05

ζ=0.5

ζ=1

ζ=10

ζ=20

ζ=30

Note: Evolution of the model generated skill premium as the ratio of wages to skilled workersover the wages to unskilled workers. The series is shown for different values parameter ζin the technology adjustment cost function G(bt, bt+1). Higher values of ζ represent higheradjustment costs.

For the case of low technological transition costs, we observe a high increase in the skill

premium very early, while at higher levels of the parameter ζ, the skill premium reacts much

slowly. The planner, endogenously chooses to slowly shift towards skill intensive technologies

when the convex cost is high in terms of inputs, and therefore, the transition is slow and skilled

workers do not see their productivity increase early on. For low values of ζ, the transition is

22

fast, and the marginal product of skilled workers reacts fast, and given the relatively low of

its stock, the price jumps much sooner.

When we observe the evolution of the skill premium in the data in Gorodnichenko and

Sabirianova Peter (2005), we observe high increases for the case of Russia, where the skill

premium increases from 4% in 1990 to 8% in 1996 and 9% in 1998. These abrupt increases

in term of the returns to education are captured in the model for the cases of relatively low

technological adjustment cost. However, in the cases where the adjustment costs are high,

the returns to education are much smoother and even fall, showing an evolution much closer

to the case of the Ukraine, where the returns to education remained between 3.7% and 3.9%

from 1990 until the year 2000.

Critical to the dynamic behavior of the model are the parameters governing the factor

intensities in goods and human capital production. Moreover, given the endogeneity of the

skill bias in the goods production technology, we have endogenous factor intensities in one of

the sectors (the goods sector). Theoretically, changing input intensities in a two sector model

can generate instability in the dynamic behavior of the model as explained in Barro and Sala-

i-Martin (2003). In the model shown here, this is not an issue given that this model does

not have a balanced growth path, and therefore we only consider the transition between an

initial condition and the steady state. The main difference with the standard model analyzed

in Barro and Sala-i-Martin (2003) comes from the definition of human capital. In this model

we do not have human capital but a fraction of skilled workers, meaning that the higher the

stock of skilled workers, the lower the stock of unskilled workers, affecting their marginal

product both in the educational and goods producing sectors. Another departure from the

standard model is that here, there is endogenous depreciation generated by the changes in

the input intensities in the goods producing sector that affects both physical capital and the

stock of skilled workers. Finally, the relative factor intensities between physical capital and

skilled workers are always higher (in the exercise) in the educational sector vs. the goods

producing sector.

23

5 Conclusion

The transition out of communism in Eastern Europe and the former Soviet Union brought

tremendous changes to the underlying economic structures. This paper proposes a model of

endogenous technological adoption, where the skill bias in production is optimally chosen.

The model is able to capture a large fraction of the features that the transition out of com-

munism displayed as the opening of a new dimension over which to optimize. Namely, if the

initial conditions where such that production was relatively biased towards the unskilled labor

force, and the initial stock of human capital was high, opening to new technologies generates

drops in physical capital, increases in the stock of skilled workers, increases in the returns to

education as well as a loss of output, at least temporarily. In other words, this model explains

the features observed starting in 1990 as the impact of a tremendous adjustment cost. The

model succeeds in explaining the salient features of the data without exogenous changes in

total factor productivity.

6 References

Bah, El-Hadj, and Brada Josef, (2009), “Total Factor Productivity Growth, Structural

Change and Convergence in the New Members of the European Union”, Comparative Eco-

nomic Studies, 51, 421-446.

Barro, Robert, and Sala-i-Martin, Xavier, “Economic Growth, Second Edition”, MIT

Press, Boston, MA.

Chari, V.V. and Hopenhayn, Hugo, (1991),“Vintage human capital, growth and the dif-

fusion of new technology”, The Journal of Political Economy, 99:6, 1142-1165.

Funk, Peter and Vogel, Thorsten, (2004), “Endogenous skill bias”, Journal of Economic

Dynamics and Control, 28, 2155-2193.

Gorodnichenko, Yuriy, and Sabirianova Peter, Klara, (2005), “Returns to schooling in

24

Russia and Ukraine: A semiparametric approach to cross-country comparative analysis”,

Journal of Comparative Economics, 33, 324-350.

Hamermesh, Daniel, (1993), “Labor Demand”, Princeton University Press, Princeton NJ.

ILOSTAT (2017), ILO.

Feenstra, Robert, Inklaar, Robert, and Timmer, Marcel, (2015), “The Next Generation

of the Penn World Table”, American Economic Review, 105(10), 3150-3182.

Fleisher, Belton, Sabirianova, Klara, and Wang, Xiaojun, (2005), “Returns to skills and

the speed of reforms: Evidence from Central and Eastern Europe, China and Russia”, Journal

of Comparative Economics, 33, 351-370.

Jovanovic, Boyan, (1998), “Vintage capital and inequality”, Review of Economic Dynam-

ics 1, 497-530.

Krusell, Per, Ohanian, Lee, Rios-Rull, Jose and Violante, Giovanni, (2000), “Capital-Skill

Complementarity and Inequality: a macroeconomic analysis”, Econometrica, 68:5, 1029-1053.

Lee, Jong-Wha, and Lee, Hanol, (2016), “Human Capital in the Long Run”, Journal of

Development Economics, 122, 147-169.

Milanovic, Branko, (1998), “Income, inequality, and poverty during the transition from

planned to market economy”, World Bank regional and sectoral studies, Washington DC.

Moscoso Boedo, Hernan, (2010), “Optimal Technology and Development”, Journal of

Macroeconomics Vol 32, 617-634.

OECD (2012), “Education at a Glance 2012: OECD Indicators”, OECD Publishing,

Paris.

Piazolo, Daniel, (2001), “Investment behavior in transition countries and computable

general equilibrium models”, Applied Economics, 33, 829-837.

Sabirianova, Klara, (2002), “The Great Human Capital Reallocation: A Study of Occu-

pational Mobility in Transitional Russia”, Journal of Comparative Economics, 30, 191-217.

Shleifer, Andrei, and Treisman, Daniel, (2005), “A Normal Country: Russia After Com-

munism”, Journal of Economic Perspectives, 19:1, 151-174.

25

Slavic Research Center Database. http://src-h.slav.hokudai.ac.jp.

Suzuki, Tomoya, (2018), “Business Cycles in Post-Conflic Serbia: The Cycle Is the Trend”,

Eastern European Economics, 56:4, 292-306.

UNESCO, (2018), UNESCO Institute for Statistics (UIS).

1 Appendix - Decentralized Equilibrium Model

1.1 Households

A set of atomistic representative households own capital and labor. They rent capital, skilled

labor and unskilled labor to the firm every period The capital and skilled labor they own is

of type b and can only be used in production in a type b firm. They make investment and

education decisions. Education is undertaken internally in the household5. That means

that the household decides how much capital, skilled labor and unskilled labor supply to the

market given prices, and the part of capital, skilled labor and unskilled labor that is not

supplied is used to produce more skilled labor for next period. Every period the type of the

physical capital and skills the household owns is given but can be changed for the future, so

the household not only chooses the evolution of the quantity of physical capital and skilled

labor but also its type for the future.

So, the problem of the representative consumer can be written as follows

max{Ct,It,Spt ,Upt ,Kpt ,Set ,Uet ,Ket ,bt+1}

∞∑t=0

βtu (Ct) (1)

5This is not a key issue. Households could buy H() in the market since it is a constant returns to scaletechnology the results would not change.

26

subject to

Ct + It ≤ (1− τst)wsbtSpt (bt) + (1− τut)wubtUpt + (1− τkt) rbtKp (bt)

+Trt

St (bt) ≥ Spt (bt) + Set (bt)

Upt + Uet ≤ 1− St (bt)

Kt (bt) ≥ Kpt (bt) +Ket (bt)

St+1 (bt+1) ≤ St [1− δs −G (bt, bt+1)] +H (Ket (bt) , Set (bt) , Uet)

Kt+1 (bt+1) ≤ Kt [1− δk −G (bt, bt+1)] + It

Where Ct, It denote consumption and investment in period t respectively. Spt , Upt and

Kpt denote skilled workers, unskilled workers and capital devoted to final production and Set ,

Uet and Ket denote skilled workers, unskilled workers and capital into education. bt indexes

the technology active in the final production sector in period t. wsbt , wubt and rbt stand for

wages for skilled workers, unskilled workers and interest rate in period t under technology

b. Taxes are denoted by τst , τut and τkt where subscript s denotes taxes on skilled workers,

u taxes on unskilled workers and k taxes on capital income. The household will also be

entitled to a transfer by the government which will be taken as given and is denoted by Trt.

Note that the household supplies to the market only one type of both skills and physical

capital and the household pays the price in terms of obsolescence when choosing what type

to supply.

1.2 Firms

Final goods producing firms can be ordered according what technology they operate, by the

parameter b. Firms operate for one period, that is they have a static problem. They rent

unskilled labor, skilled labor and capital of type b from the household in order to maximize

27

profits. In other words in every period there is demand for unskilled labor, skilled labor

and capital of every type b, 0 < b < 1. The market under which firms operate is perfectly

competitive. So problem each firm of type b solves is:

max{Spt (b),Upt ,Kpt (b)}

ptF (b,Kpt (b) , Spt (b) , Upt)

−wst (b)Spt (b)− wut (b)Upt − rt (b)Kpt (b)

So the optimal conditions for each type b firm are:

wst (b)

pt= FSp (b,Kpt (b) , Spt (b) , Upt) (2)

wut (b)

pt= FUp (b,Kpt (b) , Spt (b) , Upt)

rt (b)

pt= FKp (b,Kpt (b) , Spt (b) , Upt)

Where wst (b) stands for wages for skilled workers offered by a firm operating technology

b in period t, wut (b) stands for wages for unskilled workers offered by a firm operating

technology b in period t and rt (b) represents the interest rate offered by firms operating

technology b in period t. And pt stands for the price of final goods, which is normalized to

1. So, for every b-type firm, their maximizing behavior determines wages and interest rate

under each technology. Therefore at every moment in time we have a function of wages and

interest rate as function of the parameter b.

Note that firms in the model play a very uninteresting role. They can also be interpreted

as freely choosing the any production parameter b ∈ [0, 1], where it is necessary to hire Kp

and Sp of that type in order to produce final goods.

28

1.3 Government

The government will have a very passive role in the model. It will only collect taxes and

redistribute income through transfers. The government will run a balanced budget every

period therefore the budget constraint of the government given by:

τstwsbtSpt (bt) + τutwubtUpt + τktrbtKp (bt) = Trt

1.4 Equilibrium

Given taxes and transfers, an equilibrium is defined by a sequence of prices{{wsbt , wubt , rbr

}1b=0

}∞t=0

, allocations {Ct, It, Spt , Upt , Kpt , Set , Uet , Ket}∞t=0 and

technology parameters {bt}∞t=0, such that:

1.- Households maximize utility. That is they solve the problem defined by equation (1).

2.- Firms maximize profits. That is, for every technology parameter, equations (2) are

satisfied.

3.- Initial conditions. That is b0, S0, and K0, are given.

4.- Feasibility: Ct + It ≤ F (Spt , Upt , Kpt , bt) ; 0 ≤ bt ≤ 1 ; 0 ≤ Spt + Set ≤ 1

5.- Balanced budget of the government: τstwsbtSpt (bt) + τutwubtUpt

+τktrbtKp (bt) = Trt

Since household are identical they all make the same decision, so only one type of skills

and physical capital is supplied in the market, therefore only one firm actually operates in

the market.

29