unemployment and output dynamics in cis...
TRANSCRIPT
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ISSN 1561-2422
UNEMPLOYMENT AND OUTPUT DYNAMICS IN CIS COUNTRIES: OKUN’S LAW
REVISITED Marat Ibragimov, Javlon Karimov, Elena Permyakova
Working paper No E13/04
This project (No R11-0701) was supported by the Economics Education and Research Consortium
and funded by GDN
All opinions expressed here are those of the authors and not those of the EERC, GDN and Government of Sweden
Research dissemination by the EERC may include views on policy,
but the EERC itself takes no institutional policy positions
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JEL Classification: C26, C51, C53, E23, J64
IBRAGIMOV M., KARIMOV J., PERMYAKOVA E. Unemployment and Output dynamics
in CIS countries: Okun’s Law revisited.—Kiev: EERC, 2012.—67 p.
Keywords and phrases: GDP growth, unemployment, Okun’s Law, instrumental variable
regression, instrumental variables, exogenous and endogenous variables, instrument relevance,
robust standard errors, seasonality
Acknowledgements. Authors gratefully acknowledge the financial support from Economics
Education and Research Consortium (EERC), grant No R11-0701. We sincerely thank the panel of
experts, who took part in 30th, 31th and 33th workshops organized by EERC, for fruitful
comments and suggestions that improved earlier drafts of our proposal. Especially, we are heavily
indebted to Diana Weinhold for detailed discussions, comments, and guidance. We are responsible
for all remaining errors.
Marat Ibragimov
Department of Higher Mathematics, Tashkent State University of Economics
Associate Professor
Tel: (+998 71) 248 78 30
E-mail: [email protected]
Jovlon Karimov
Department of Higher Mathematics, Tashkent State University of Economics
Senior Lecturer
Tel: (+998 71) 2454463
E-mail: [email protected]
Elena Permyakova
N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University
Researcher
Tel: +7 89033146431
E-mail: [email protected]
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CONTENT A. Summary ..................................................................................................................................... XI
B. Introduction ................................................................................................................................... 1
C. Review of the literature ................................................................................................................. 4
D. Relationship between economic growth and change in the unemployment rate .......................... 6
E. Model specification and estimation results ................................................................................... 8
1. Data and notation used ............................................................................................................... 8
2. Problems in data ......................................................................................................................... 8
3. Methodology ............................................................................................................................. 12
4. Empirical results ....................................................................................................................... 12
4.1. Russia ............................................................................................................................ 12
4.1.1. Seasonal components of unemployment and economic growth in Russia ......... 12
4.1.2. Estimates of Okun’s model ................................................................................. 13
4.1.3. Further results: Analysis of the relationship between unemployment and
economic growth using the concept of elasticity .......................................................... 18
4.2. Uzbekistan ...................................................................................................................... 23
4.2.1. Seasonal components of unemployment and economic growth ........................ 24
4.2.2. Estimates of Okun’s model ................................................................................. 24
4.3. Ukraine .......................................................................................................................... 25
4.4. Belarus ......................................................................................................................... 26
4.5. Moldova ........................................................................................................................ 26
4.6. Kazakhstan ..................................................................................................................... 27
4.7. Cross-country comparative analysis .............................................................................. 28
F. Conclusion ................................................................................................................................... 31
G. Bibliography ................................................................................................................................ 38
Appendix A. Data and notation ........................................................................................................ 41
Appendix B. Methodology ............................................................................................................... 43
B.1. The method of instrumental variables (IV) .................................................................. 43
B.2. Confidence intervals for elasticity using the delta method .......................................... 45
Appendix C. Confidence and prediction intervals for a regression .................................................. 48
Appendix D. Confidence and prediction intervals for the regression of changes in the
unemployment rate on GDP growth in CIS countries: Estimates for Russia, Belarus, Kazakhstan,
Moldova, Ukraine and Uzbekistan .................................................................................................... 50
Appendix E. Figures and Tables ...................................................................................................... 57
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A. SUMMARY
Okun’s law is a well-known relationship between the change in the unemployment rate and
output growth. The main objective of the study is to provide a rigorous econometric analysis of
Okun’s law for several CIS countries using different models and econometric methods. The paper
further focuses on the analysis of the behavior of unemployment and Gross Domestic Product in
Russia, Belarus, Kazakhstan, Moldova, Ukraine and Uzbekistan in different periods of their
economic development during 2000-2010.
The traditional approach to Okun’s law estimation using OLS regressions does not account
for possible endogeneity of regressors and the implied inconsistency of the estimates obtained.
These problems point out to incorrectness of applications of the standard OLS estimation
techniques. Our study addresses these issues by using econometrically justified instrumental
variable regression methods.
The report provides the results and discussions on the practical use of Okun’s relationships
for evaluation of average effects of economic growth on the unemployment rate, and vice versa;
importance of accounting for confidence intervals in applications of Okun’s models to economic
development analysis and cross-country comparisons; as well as those on the value of the models
for economic forecasting and policy decisions. We also discuss in detail the results of formal
econometric tests and economic motivation for validity of instrumental variables used in the study.
The formal econometric tests, together with economic arguments, allow us to determine the most
appropriate Okun-type models for each of the CIS countries under consideration.
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B. INTRODUCTION
Compared to other markets, the labor market is more affected by social and political
factors as well as by economic and financial crises and shocks. Naturally, labor supply and,
therefore, the price of labor, significantly depend on the dynamics of the total population and the
employable population. Labor demand and supply are affected by age, education, gender
composition of the population, the mobility of the workforce in the country, the possibility of
migration between countries, as well as by the level of technology used in the production
process. Economies and the balance on their labor markets are also greatly influenced by import
and export of labor resources. While import of labor increases the production of economic goods
that are characterized by relatively low marginal revenue from production (primarily public
goods and goods with large positive externalities, such as public transport, town planning, etc.),
labor export significantly increases national income due to a large inflow of transfers from
citizens working abroad. Moreover, export of labor reduces the pressure of unemployment on the
economy and thus decreases social tensions. If the problems associated with labor import and its
consequences are relevant for Russia and Kazakhstan, the problems associated with labor surplus
are important primarily for post-Soviet Central Asia, the Caucasus, Belarus, Moldova and
Ukraine. In Central Asia, the situation on the labor market is further complicated by high birth
rates and growth of the economically active population.
The Russian labor market is the most studied and, at the same time, the most nonstandard
one among the labor markets of the CIS countries (see Gimpelson and Kapeliushnikov, 2005,
2008, 2011, and Gimpelson et al., 2010). In all the countries of the CIS, including Russia, a
major role in the production of wealth is played by the shadow component of resource and goods
markets. The shadow component of the markets includes, in particular, import and export of
unrecorded labor, shadow wages as well as shadow production and allocation of goods.
Naturally, the unemployment rate is an important factor that affects the balance in labor
markets and economic activity. Unemployment reveals its role as a stabilizer of structural
macroeconomic imbalances through its effects on the labor market equilibrium. Identification of
possible realizations of the pair of indicators <change in employment, change in total output>
under the existing socio-political, economic and social relations in a country is particularly
important for its political, economic and social security. Despite the existing research and
recommendations of the IMF and other regulatory organizations on these indicators,
unemployment adjustment and parallel creation of new jobs is an extremely difficult process.
Social policy has traditionally been considered as an important part of macroeconomic
policy in the post-Soviet countries. The population of the former Soviet Union still well
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remembers social security that existed in the USSR and contrasts it with the current need to pay
for health care and higher education, etc. Unemployment rate and the necessity to reduce the
excess pressure of their economically active population are some of the main problems faced by
the governments of the former Soviet countries. This is due to the nature of emerging and
transition labor markets that inherently have low labor mobility, high differentiation of wages in
different sectors of the economy, low wages in the formal economy and high inflation.
The main objective of the project is to provide the analysis of the dynamics of
unemployment and economic growth in CIS countries using different models and econometric
methods. The study presents a rigorous econometric analysis of the relationship between the
GDP growth and unemployment, commonly referred to as Okun’s law, in Russia, Belarus,
Kazakhstan, Moldova, Ukraine and Uzbekistan.
The project focuses on formal econometric analysis of unemployment and output
dynamics in several countries of the former USSR. A particular focus of the analysis is on the
study of Okun’s law that describes the relationship between changes in unemployment and
economic growth rates in a country. One version of the statistical relationship has the following
simple form:
Δ𝑢=α - β·y, (1)
where Δ𝑢=U-U-1 and 𝑦 = 𝑌−𝑌−1𝑌−1
denote, respectively, a change in the unemployment rate and the
output growth rate, and α denotes the constant term. The slope parameter β in (1) is usually
referred to as Okun’s coefficient. The coefficient β may be interpreted as follows: on average, a
1% increase in the output growth rate y is associated with a decrease in the unemployment rate
by β percent compared to the previous period.
It should be emphasized that the coefficient β is different from the coefficient of elasticity
of unemployment U with respect to the volume of total output Y (see Section 4.1.3). The factors
that affect the value of the coefficient β include labor market institutions (such as legislative
employment protection, unemployment benefits, employment contracts and wage flexibility) and
episodic events, such as the economic and financial crises, changes in housing prices, trade
shocks, policy changes and economic and financial uncertainty, among others. The coefficient β
and the effects of the above factors on the unemployment dynamics usually vary in different
stages of economic development, as well as in phases of recession and recovery (see Gabrisch
and Buscher, 2006, and IMF, 2010). The differences in the values of the coefficient β across
countries and over time are important because they reflect the influence of several key factors on
the dynamics of unemployment and labor markets.
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Unfortunately, the approach based on Okun’s law estimation using OLS regressions used
in the most of studies in the literature works only under the very strong assumption of strict
exogeneity of regressors. The exogeneity assumption is usually violated in practice since a
change in the unemployment rate Δ𝑢 leads to a change in future output. This points out to
simultaneous relationship between the variables, reverse causality and regressor endogeneity. To
address possible violations of regressor exogeneity assumptions, we provide a regression
analysis using instrumental variables (IV) for the regressor y. We further use robust estimates for
standard errors of regression coefficients obtained to account for possible heterogeneity and
autocorrelation in the regression error.
As discussed in the next section, some of recent studies suggest that relations between
unemployment and output similar to Okun’s law can be identified not only for developed
countries but also for transition economies. In turn, together with the Phillips curve, Okun’s law
for unemployment and output forms the basis for the model of aggregate supply in
macroeconomic theory.
The Phillips curve was subject of numerous tests for different economies. A number of
recent studies have also pointed out several problems with Okun’s law. First, it appears that
Okun’s coefficient is different in different economies. Second, in addition to changes in the
unemployment rate, the GDP growth rate is significantly affected by other labor market
variables, such as changes in hours worked, productivity, the number of employees,
technological changes and innovations, among others. 1
Among other results, the project provides the results of rigorous formal tests of statistical
hypotheses related to Okun’s law and unemployment and output dynamics. Our study aims not
only at estimation of Okun’s model for economies considered, but also at evaluation of
confidence intervals for realizations of the unemployment rate and the GDP growth rate
determined by a combination of different quantitative and qualitative factors. In particular, in
addition to estimation of Okun’s coefficients, we also focus on the analysis of their confidence
intervals and discuss implications of the analysis for economic development analysis and cross-
country comparisons. A similar analysis is also presented for regression confidence and
prediction intervals, together with the discussion of their implications for unemployment and
economic growth forecasting.
1 See, for instance, Prachowny (1993) who studies the effects of changes in the number of weekly hours worked and those in production capacity on output changes. He finds that, in addition to changes in the unemployment, the above variables significantly affect changes in the output volume and provides estimates of their effects.
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C. REVIEW OF THE LITERATURE
The relationship between unemployment and output referred as Okun’s law was first
proposed by Okun (1962). Okun (1962) empirically established negative correlation between
changes in unemployment and the change in aggregate output. Using different models and
versions of the relationship between unemployment and output, Okun showed that, after the
World War II, in the US economy, a 3% increase in output was associated with a 1% decrease in
unemployment. Subsequent empirical studies have confirmed the statistical relationship between
unemployment and aggregate output in Okun’s law for other developed economies.
Following the pioneering work of Okun, the relationship between the change in the
unemployment rate and output growth was examined by many economists, including Smith
(1975), Gordon (1984), Knoester (1986), Kaufman (1988), Prachowny (1993), Weber (1995) and
a number of others. Although the majority of the studies have focused on the US economy, the
negative correlation between changes in unemployment and aggregate output was also tested for
other countries. Knoester (1986) and Kaufman (1988) find differences in Okun’s coefficients for
different countries. Moosa (1997) provides the estimates of parameters of Okun’s model for a
number of developed countries, including the United States, Canada, France, Germany, Great
Britain, Italy and Japan. Izyumov and Vahaly (2003) discuss estimates of aggregate (and thus
averaged, see the discussion in Section F) Okun-type models for 25 transition economies in the
90’s that are divided, mostly due to data limitations, into two groups of “reform leaders” and
“reform laggards”. Gabrisch and Buscher (2006) focus on the analysis of the relationship
between unemployment and aggregate output in several post-communist countries (Czech
Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovak Republic and Slovenia). Harris
and Silverstone (2001) provide estimates for a modified form of Okun’s law for 21 developed
(mostly European) economies. Arabaci and Arabaci (2010) obtain very interesting results on
correlation between changes in the unemployment rate and output in Turkey using quarterly data
for the period from 1999 to 2009. Their results show that there is a significant asymmetry in the
relationship between changes in unemployment and output, especially in phases of economic
downturn. IMF (2010) presents a detailed review and estimates of Okun’s models, together with
a discussion of factors affecting them, for several developed countries and periods of economic
recession and recovery.
Akhundova et al. (2005) determine the form of Okun's law for the Russian Federation
using data for the period from 1994 to 2004. According to the results obtained by the authors, in
Russia, a 1% increase in the real GDP was associated with a 0.12% decrease in the
unemployment rate before 2000 and with a 0.25% decrease in the unemployment rate after 2000.
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Akhundova et al. (2005) conclude that “first, both the real GDP and the unemployment rates
appeared to be rather persistent indicators that strongly depend on their values in the previous
period. A natural consequence of this situation is given by the weak influence of the variables
considered on each other. Second, the characteristics of dependence under study are significantly
affected by the 1998 crisis that has changed the trajectory of the dynamics of the unemployment
rate and that of the real GDP.” The authors have also indicated that “the inflexibility of the
Russian labor market leads to persistence in changes of the unemployment rate and to absence of
the immediate response of the latter to changes in output.”
One should note that, similar to the above discussion in Akhundova et al. (2005), a
number of studies in the literature emphasize relatively stable (or, more precisely, highly inertial
or “sticky”) employment as one of the main long-term distinctive features of the Russian labor
market (see, among others, Gimpelson and Kapeliushnikov, 2011, and references therein). The
(un)employment inflexibility, in particular, distinguishes the conditions on the Russian labor
market even from developed and transition countries and regions for which very pronounced
labor market stickiness is also observed.2 In addition, as discussed in a number of works, the
labor markets in most of the CIS countries are, naturally, strongly influenced by economic
conditions in Russia and also operate in a way similar to the Russian labor market (see, among
others, the discussion in Commander and Tolstopyatenko, 1997; Boeri and Terrel, 2002, and
Gimpelson and Kapeliushnikov, 2011).
Gimpelson and Kapeliushnikov (2011) further present an excellent detailed qualitative
overview of the evolution of the Russian labor market over two decades of transition. In
particular, the paper discusses in detail the major factors and determinants behind persistence of
“the Russian way in labor market adjustment” with highly inertial employment (see Layard and
Richter, 1994) that “survived several shifts in macroeconomic regimes, a few attempts at partial
reform, and four external macroshocks” (Gimpelson and Kapeliushnikov, 2011), including the
2008 global economic and financial crisis. The authors argue that the main explanations of
persistence of the Russian model of labor market adjustment consist in flexible working time
(e.g., with shifts of firms’ personnel into administrative leaves or into short-time work during
economic downturns and recessions) and downward wage flexibility used by firms to contain
labor costs in downturns (e.g., using inflationary depreciation of real wages, cuts in premiums
and bonuses that constitute a significant part of total wage payments, wage arrears and shrinkage
in undeclared payments and shadow wages). In addition, Gimpelson and Kapeliushnikov (2011)
2 See, for instance, Soltwedel et al., 2000, who discuss labor market stickiness as labor market conditions that do not change quickly in response to changes in supply and demand in several European countries, including Finland, eastern Germany, Ireland, southern Italy, and southern Spain.
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discuss several institutional factors explaining the observed (reverse) employment/wage
asymmetry in the Russian labor market and emphasize, in particular, the role of weak
enforcement of major wage and employment regulations in Russia.
Most of the studies of Okun’s law in the literature and those by regulatory agencies like
the above extensive analysis by the IMF are based on estimates obtained using the OLS. The
obtained estimates of Okun’s models are often used, in particular, for the analysis of
development of labor markets and their changes over time, cross-country comparisons of labor
markets as well as for unemployment or economic growth forecasting.
However, the OLS approach to estimation of Okun’s models is based on strong
assumptions such as strict exogeneity of real output. The use of the OLS approach may lead to
incorrect (in statistical terms, inconsistent) estimates if the exogeneity assumption is violated, as
is likely to be the case in reality (see, among others, Ch. 12 in Stock and Watson, 2007, and the
discussion in Sections D and E.3).
One of the few works that explores the possibility of endogeneity of real output in the
dynamic version of Okun’s law is the paper by Gabrisch and Buscher (2006). Gabrisch and
Buscher (2006) estimate Okun’s law for post-communist countries of Eastern Europe using
instrumental variable regressions to address the possible endogeneity problems. Gabrisch and
Buscher’ (2006) study, however, does not include Russia and other CIS countries.
It is interesting to work Ball, Leigh and Loungani (2012) on the stability of Okun's Law.
They find that Okun’s Law is a strong and stable relationship in most countries, one that did not
change substantially during the Great Recession. However Okun coefficients differ substantially
across countries. This variation is partly explained by idiosyncratic features of national labor
markets, but it is not related to differences in employment protection legislation.
D. Relationship between GDP growth and change in the unemployment rate
Many studies in the literature have focused on the analysis of factors affecting economic
growth in different countries (see, among others, Barro and Sala-i Martin, 2004, Howitt and
Weil, 2008, Steckel, 2008, the discussion in Ibragimov and Ibragimov, 2010, and references
therein). The main determinants of economic growth are, naturally, capital, technology and
efficiency. In addition, a number of studies have stressed the role of geographical and cultural
factors, economic policies and institutions as fundamental causes of differences in economic
growth rates across countries. Besides the above variables, good statistical characteristics in
explanatory models for output growth rates were obtained for such factors (regressors) as the
share of investment in GDP, initial income, initial level of human capital, population growth
rates, employment levels, changes in unemployment and shocks caused by disasters and crises.
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An important problem that is rather less researched in the literature is given by the analysis of the
effects of shadow economy on economic growth and unemployment. A major difficulty in such
analysis is that it is impossible to quantitatively estimate the contribution of shadow economy to
growth (see also the discussion in Section E.2). Moreover, one can only approximately estimate
the share of shadow economy in a country’s total output. In addition, a significant role in a
country’s economic growth and its social factors, including the unemployment rate, is played by
the volume of labor export and import, including their shadow components, and also by
government immigration policies.
Many studies agree on the negative correlation between the GDP growth rates and
changes in the unemployment rates (see, among others, the discussion in IMF, 2010, Ch. 3, and
references therein). The negative correlation is observed, in particular, in the case of Russia (see
Figure E2). The main question is to quantify the negative relationship between output growth
and changes in unemployment and to analyze its main determinants and explanations.
Suppose that the GDP growth rate and the change in the unemployment rate are
determined by a large set of quantitative and qualitative factors X = (x1 ,..., xk,...). In other words,
suppose that, at each time period t, the GDP growth rate y and the change in the unemployment
rate Δu are jointly determined from the following system of equations:
� 𝑦𝑡 = 𝑓(𝑥𝑡1, … , 𝑥𝑡𝑘, … ),∆𝑢𝑡 = 𝑔(𝑥𝑡1, … , 𝑥𝑡𝑘, … ). (2)
Thus, at time t, one observes only a pair (yt, Δut) of realizations of the GDP growth rate
and the change in the unemployment rate, whose values are determined by a combination of the
factors Xt. E.g., the scatter plot of changes in the unemployment rate and the corresponding GDP
growth rates (see Figure E2) essentially depicts, in some sense, the equilibrium values of the
above variables each period (the situation is similar to the analysis of demand and supply curves
using the equilibrium price and quantity values, see Ch. 12 in Stock and Watson, 2007).
It is of interest not only to assess the effects of changes in the unemployment rate on
output growth (that was the main problem studied by Okun) or, vice versa, that of output growth
rates on unemployment changes. It may be tempting to influence economic growth through a
reduction in unemployment. Or, conversely, motivated by social goals, it may be tempting to
influence the unemployment rate through changes in economic growth. However, it is quite
possible that there does not exist a causal relationship between these variables for a given
economic system (see the summary of the results of this study in Section E). For instance, under
administrative methods of economic activity coordination, unemployment does not affect
economic growth at all by definition. The very notion of unemployment is nonexistent under
these coordination methods: the state can administratively achieve any employment level that is
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limited only by the number of population and that of employable people. Classical examples of
the above situation are given by the economies of the USSR and other countries of the
communist bloc. The USSR even had the law “On social parasitism” that required every citizen
to work. The country always had labor shortages, but not surpluses.
Nevertheless, many authors indicate existence of a relatively stable statistical relationship
between output growth and changes in the unemployment rate without discussing other factors
that affect these variables (see, for example, Gabrish and Buscher, 2006, and references therein).
Gordon (1984, p. 539) argues that “this relationship has remained popular in macroeconomic
analysis both because it has been sufficiently stable and reliable in the past two decades to
deserve being labeled a law and also because it short-circuits the rather complex identity that
links output and unemployment”.
In what follows, we leave aside the question whether there is a causal relationship
between changes in the unemployment and the rate of economic growth. Instead, for a given
country, we try to determine the intervals, where each of the indicators y and Δu belongs to with
a specific confidence probability for a given value of the other indicator (that is permissible in
terms of the determinants X in (2) for the latter variable). In other words, instead of inexplicit
dependence between y and Δu in relation (2) with an unknown form and characteristics, we focus
on estimation of the explicit relationship y= h(Δu) between the variables. More precisely, we
focus on estimation of the parameters and their standard errors and confidence intervals in the
latter explicit relation in form (1) or its analogues using rigorous econometrically justified
inference methods.
E. Model specification and estimation results
1. Data and notation used
The notation for the main variables considered and the results of tests for stationarity of
time series dealt with in the study are described in Appendix A.
2. Problems in data
A major difficulty in estimation of parameters in model (1) and its analogues using data
on Δu and y is that the regressor y is typically correlated with the error term ε, that is the
regressor is endogenous. Following the standard terminology, variables correlated with the error
term are called endogenous variables, and variables uncorrelated with the error term are called
exogenous variables (see Ch. 12 in Stock and Watson, 2007).
If y and ε are correlated, then the OLS estimates of the regression parameters are biased
and inconsistent. Inconsistency of the OLS estimates means that their bias persists and does not
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vanish even if the sample size is very large. Therefore, regressor endogeneity presents a problem
whether the sample size is large or small (see, among others, Ch. 6 in Stock and Watson, 2007).
Tsyplakov (2007) discusses the following most common reasons for correlation between
a regressor and the regression error, or in other words, threats to internal validity of the OLS
regression analysis (see also Chs. 9 and 12 in Stock and Watson, 2007):
• omitted variables that are correlated with the regressor used;
• regressors measured with errors (“errors-in-variables”);
• simultaneous relationships among the variables (simultaneous causality);
As in Tsyplakov (2007) and Chs. 9 and 12 in Stock and Watson (2007), we briefly
discuss each of the above threats to internal validity of the OLS.
1. Omitted variables
The change in the unemployment rate is influenced not only by output growth, but also
by a number of other different factors. Therefore, (1) contains unobserved variables q1, …, qm:
Δu = α – βy +γ1 q1 +…+ γm qm + ν. (3)
Suppose that, in equation (3), the error term ν is uncorrelated with y and qi, i = 1 ,.., m. Since the
variables q1, …, qm are unobserved, instead of regression (3), one has to estimate the regression
Δu = α – βy + ε (1’)
with the error ε that has the form ε= γ1 q1 +…+ γm qm + ν. If the regressor y is correlated with the
unobserved variables, it will assume a part of influence of the variables q1, …, qm on the
dependent variable Δu. Therefore, the OLS estimates of the coefficients in (1’) are biased and
inconsistent.
2. Errors-in-variables
If there are measurement errors, the estimation results may differ from reality. If the
variables in a regression are measured with error, the results of regression estimation using the
OLS are biased and inconsistent. This is due to the fact that the measurement error of regression
variables becomes a part of the regression error. As a result, the measurement errors are
contained both in the regressors and the regression error, so that the regression error and
regressors are correlated with each other.
This problem is very important in the case of output and unemployment. We mention
only some of the typical causes of errors in measurement of these variables.
• Official data on the volume of national income does not fully account for its shadow
component. Since the characteristics of shadow economy are unobservable, they can be
estimated only indirectly. Typically, statistical authorities adjust the level of national income
upward using available estimates of the shadow economy (see Kulekeev, 1997, and
Schneider and Enste, 2002). Schneider and Enste (2002) discuss estimates of the shadow
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economy in the range of 21-30 percent of the official GDP for transition economies. These
estimates are for the period from 1988 to 2000 and may have since changed. Naturally,
shadow economy affects economic growth. Theoretical and empirical studies do not provide
convincing conclusions on these effects and their explanations. According to several studies,
the shadow economy constrains the growth of GDP. In particular, these studies argue that a
decrease in the volume of shadow economy increases tax revenues by stimulating an increase
in public expenditures, especially on infrastructure and services. This supports production
expansion, resulting in an increase in overall economic growth. An opposite view is that the
informal sector is more competitive and efficient compared to the formal sector, so that the
shadow economy stimulates overall economic growth. Some empirical studies show that at
least two thirds of income earned in the shadow economy is quickly spent in the formal
economy. The two thirds of the value added from the shadow economy in Germany and
Austria would not have been produced at all if it were not for the shadow economy. In the
UK in 1960-1984, the revenue in the shadow economy significantly increased consumer
spending, especially on durable goods and services. The above consumer spending positively
affects economic growth and income from indirect taxes (the above examples are discussed
in detail in Schneider and Enste, 2002, and references therein; the methodology for
evaluating the parameters of the unobserved economy for CIS countries is discussed, in
particular, in reports of representatives of statistical agencies of these countries at the
Seminar on Statistical Estimation of Unobserved Economy, Sochi, October 16-20, 2000 -
Joint OECD-Eurostat-Russian Statistical State Committee Workshop, 2000).
• Estimation of the unemployment rate involves measuring the aggregate labor force and the
number of people employed in the formal and informal economies. However, similar to
many other characteristics of the informal economy, the latter variable is unobservable and
can be determined only indirectly. Therefore, it is impossible to correctly estimate the
number of people employed in the informal (including shadow) economy. Moreover, this
situation is complicated by the fact that some workers take on a second, shadow work, and
conduct it after or even during their work at official positions. This is primarily due to low
official labor compensation.
At the same time, the number of the registered unemployed significantly differs from the
actual number of the unemployed. This is due, in particular, to the fact that, in many post-
Soviet countries such as Uzbekistan, the transaction costs of registering as an unemployed
are large, and the unemployment benefits are very small.
In some countries (Russia, for example), some large employers prefer not to lay off
workers, but transfer them to part-time jobs or provide unpaid leaves of absence for
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indefinite periods. Moreover, the book by Gimpelson and Kapeliushnikov (2008) argues that
this is not only a policy common among large employers, but is also one of the main
characteristics of the Russian labor market (see also the discussion in Section C and
Gimpelson and Kapeliushnikov, 2011). This practice further complicates correct calculations
of the unemployment rate.
3. Simultaneous causality
Simultaneity occurs when two or more variables affect each other, so that their values are
determined endogenously from a system of equations (see also Section 4.1.2). In the case of the
unemployment rate and output, one observes their simultaneous, “equilibrium”, values each
period. In order to identify the model parameters using the data on output growth and changes in
the unemployment rate, one has to form a cross-section of all the factors that affect these
variables, that is, to create a “ceteris paribus” situation. Otherwise, there exists the problem of
endogeneity of regressors that leads to biased and inconsistent estimates of regression
coefficients (see a discussion of similar problems in estimation of demand and supply using the
data on equilibrium values of good prices and quantities in Ch. 12 in Stock and Watson, 2007).
More generally, possible regressor endogeneity is an especially important problem in
time series regressions. As discussed in Section 15.7 in Stock and Watson (2007), “regressors
can be correlated with the error term for several reasons, but with economic time series data a
particularly important concern is that there could be simultaneous causality, which results … in
endogenous regressors”. In many time series regressions, both the current and past (lagged)
values of the variables dealt with are likely to be correlated with the error term (see Tsyplakov,
2007 and Section 15.7 in Stock and Watson, 2007). Similar to Stock and Watson (2007), this
may be illustrated using the example of the Phillips curve estimated by a regression of the
change in the rate of inflation against the lagged inflation changes and unemployment rates.
Since the past unemployment rate was simultaneously determined with past values of inflation
(similar to the discussion in Section D for unemployment and output growth rates in Okun’s
law), the other factors that determine inflation contained in the error term are correlated with past
values of the unemployment rate. This means that the unemployment rate is not exogenous in the
Phillips curve regression.
Similar to the example of the Phillips curve, time series regressions often include lags of
the dependent variable. For time series regressions with autocorrelated errors, the lags of the
dependent variable are likely to be correlated with the error (Tsyplakov, 2007) leading to
inconsistent OLS estimates of the time series regression parameters.
One should also note that, under the regressor exogeneity condition, the OLS estimates in
a time series regression are consistent even if the error is autocorrelated. However, in general, the
12
autocorrelation in the error term leads in inconsistency of the usual OLS standard errors (see, for
instance, Section 15.4 in Stock and Watson). Therefore, it is important to use heteroskedasticity
and autocorrelation consistent (HAC) standard errors in time series regressions with
autocorrelated errors. Alternatively, one can apply other robust inference methods, such as those
based on time series regression estimates for different groups of time periods (see Ibragimov and
Müller, 2010).
One should note here that the estimates of Okun’s law presented in Ch. 3 of IMF (2010)
do not take into account possible correlations of the lagged dependent variable with the error and
the implied inconsistency of estimates.
Consistent estimates of parameters in econometric models with (possible) correlations
between the independent variables and the regression error can be obtained using the approaches
and methods based on the use of instrumental variables (see, among others, Ch. 12 in Stock and
Watson, 2007, and also Anatolyev, 2007, Ebbes, 2007, Pagan, 2007, Pollock, 2007, Sims, 2007,
and Tsyplakov, 2007).
3. Methodology
See Appendix B.
4. Empirical results
4.1. Russia
Following Appendix A, throughout the paper, we use the notation described below. The
data referred to below is quarterly.
Yrussia denotes Russia’s GDP in current prices, 1995:1-2011:1;
yrussia is the GDP growth rate in Russia, 1995:2-2011:1;
Urussia denotes the unemployment rate in Russia, shares, 2003:1-2010:4;
Δurussia = U - U-1 is the change in the unemployment rate in Russia, shares, 2003:2-
2010:4.
Consider the dynamics of the quarterly GDP growth rate yrussia and changes Δurussia
in the unemployment rate in Russia (see Figure E.1). One can observe that the dynamics of these
indicators is influenced by seasonal factors, as well as by the 2008 global economic and financial
crisis.
4.1.1. Seasonal components of unemployment and economic growth in Russia
The GDP growth rates and changes in the unemployment rate and in Russia have
seasonal components. In order to detect seasonality, we use the dummy variables q1, q2 and q3
that correspond to quarters of a year:
13
𝑞𝑖𝑡 = �1, 𝑖𝑓 𝑡 = 4𝑛 + 𝑖;0, 𝑖𝑓 𝑡 ≠ 4𝑛 + 𝑖,
where i = 1, 2, 3, and n is an integer. In other words, the variable qit takes value one if the period
t = 1, 2, ... corresponds to the i-th quarter of the (n+1)th year. Otherwise, the variable qit is zero.
Table E.1 provides the estimates of the regression of Δu and y on the variables q1, q2, q3 and
their statistical characteristics. According to Table E.1, with a significance level of 5%, one can
indicate that the GDP growth rate in the first quarter of a year in consideration is smaller by 8.6
to 20.8 percentage points compared to that in the fourth quarter. Similarly, the GDP growth rate
in the second quarter is greater by 3.3 to 12.5% and that in the third quarter is greater by 5.3 to
14.2% compared to the fourth quarter. Compared to the fourth quarter of a year under
consideration, the change in the unemployment rate in the first quarter is greater by 0 to 1
percentage point, that in the second quarter is smaller by 1 to 2%, and the change in the
unemployment rate in the third quarter is smaller by 0.3 to 1%.
4.1.2. Estimates of Okun’s model
Consider the change in the unemployment rate in Russia Δurussia as the dependent
variable.
Due to endogeneity of regressors, we conduct the TSLS estimation using the instrumental
variable method (see the discussion in Section 3.1 and Table 4.2). According to the estimates in
Table 4.2 (Model 1),
Δurussia=0.0039 – 0.0856 yrussia – 0.4045Δurussia(-1). (4)
Relation (4) has the form
Δut=α+βyt+γ Δut-1,
where α=0.0039, β= - 0.0856 and γ= - 0.4045. This implies
Δut=α(1+ γ+ γ2+…+ γt-1)+ β(yt+ γ yt-1+ γ2 yt-2+…+ γt-1 y1)+ γt Δu0,
or
Δut=𝛼(1−𝛾𝑡)1−𝛾
+ βyt+ β (γ yt-1+ γ2 yt-2+…+ γt-1 y1)+ γt Δu0. (5)
Consider the case |𝛾| < 1 (this is confirmed by the analysis of stationarity for Δurussia,
see the table in Appendix A). For t∞ we have γt0 and for large t one has
Δut≈𝛼1−𝛾
+ βyt+ β (γ yt-1+ γ2 yt-2+…+ γt-1 y1).
If we restrict ourselves only to the first three lags of quarterly GDP growth rates, then
Δut≈𝛼1−𝛾
+ βyt + β(γ yt-1 + γ2 yt-2 + γ3 yt-3). (6)
Formula (6) covers 4 quarters, that is one year.
Consider now the TSLS estimates for Model 2 in Table 4.2:
14
Δurussia=0.00336-0.0747 yrussia, (7)
Table 4.2. TSLS regressions for the change in unemployment and the GDP growth rate
in Russia
Regressors Δurussia [95% Conf. Interval] Regressors Δurussia [95% Conf.
Interval] Model 1 Model 2
Yrussia -0.0856** (0.0104) [-0.107; -0.064] yrussia -0.0747**
(0.0109) [-0.097; -0.052]
Δurussia(-1) -0.4045** (0.1063) [-0.623; -0.186] Const 0.00336**
(0.0013) [0.0008; 0.006]
Const 0.0039** (0.0012) [0.0015; 0.006]
R2 0.757 0.596 F(m,n-m-1) F(2, 27) = 34.31 F(1, 29) = 47.22 Prob>F 0.0000 0.0000 Instrumental variables pcrudeoil, q1, q2, q3 pcrudeoil, q1, q2, q3 First stage F-statistic F(4, 25) = 105.21 F(4, 26) = 77.25 Overidentifying restrictions J-test and p-value
0.00 1.00
0.00 1.00
Note: 1) Standard errors are given in parentheses under the coefficients; 2) ** denotes significance at the1%
level.
Using the method described by Yakovleva (2008) и Draper and Smith (1981), we
construct confidence intervals for regression (7) (see Appendix C). The 95% confidence intervals
for regression (7) are provided in Figure D7 in Appendix D. These intervals may be considered
as 95% confidence intervals constructed for the average value Δ𝑢𝑟𝑢𝑠𝑠𝚤𝑎� that corresponds to a
given value of yrussia. One can see from the figure that, for a wide range of GDP growth rates,
the corresponding average values of changes in the unemployment rate in Russia are
indistinguishable at the 5% significance level. For instance, for the GDP growth rates in the
range from zero to 7.5%, the confidence intervals for the average values of Δ𝑢𝑟𝑢𝑠𝑠𝚤𝑎� intersect.
That is, with the significance level (probability of error) of 5% (or less), one cannot assert that
the average values of changes in the unemployment rate are different from each other.
The situation is even worse for forecasting changes in the unemployment rate in Russia.
Figure D8 in Appendix D presents the 95% prediction intervals for the values of Δurussia that
correspond to given values of yrussia (see the discussion of the difference between confidence
and prediction intervals in Draper and Smith, 1981, Ch. 1, Section 1.4). For all GDP growth rates
ranging from -20% to 20%, the prediction intervals for Δurussia intersect. Therefore, one cannot
econometrically justify the unemployment rate forecasting using only Okun’s law and the GDP
growth rates.
15
We now discuss Okun-type models that, in addition to change in the unemployment rate,
GDP growth rate and their lags, also include other variables. Our goal is to obtain the most
appropriate model according to its statistical characteristics. The regressors used for the
dependent variable Δurussia are given by combinations of the variables {yrussia, pgold, q1, q2,
q3}, where yrussia is the Russian GDP growth rate; pgold is the chain price index for gold; and
q1, q2 and q3 are dummy variables defined in Section 4.1.1 that correspond to the first, second
and third quarter of a year (as before, other variables used in this section are described below and
in Appendix A).
Table E2 provides the results of TSLS estimation of Okun-type models for Russia. As
instrumental variables for the regressor yrussia, we use combinations of the variables {ychina,
pcrudeoil, pgold, q1, q2, q3}. Here ychina is the GDP growth rate in China and pcrudeoil is the
chain price index for crude oil. Table E2 and other tables on the results of TSLS estimation
discussed in this Section and throughout the report use the following notation: n is the number of
observations considered (the sample size); m is the number of regressors; F(m, n-m-1) is the
calculated value of the F-statistic for the coefficient of determination R2; and Prob is the
probability of the first-type error (the p-value) of the F-test on R2 for the data under consideration
(that is, Prob is the probability of rejecting the true null hypothesis on equality of the coefficient
of determination to zero: H0: R2 =0 for the given data).3
As discussed in Appendix B.1, relevance of the instrumental variables, that is, their
strong correlation with the regressor yrussia is assessed using the first stage F-statistic. The latter
is the F-statistic for the test of the null hypothesis: H0: b1= ... =bk=0, where b1, ..., bk, k ≤ 6 are the
coefficients of the first stage regression of yrussia on the instrumental variables from the set
{ychina, pcrudeoil, pgold, q1, q2, q3}. The values of the first stage F-statistics in Models 1-4
and 6 in Table E.2 are greater than the rule of thumb value 10 discussed in Appendix B.1: F(m,
n-m-1)≥10. That is, the F-statistics are sufficiently large to reject the hypothesis H0 at the 1%
significance level for the models (see Stock and Watson, 2007, Ch. 12). Following the rule of
thumb for checking for instrument relevance, we thus conclude that the instruments in Models 1-
4 and 6 in Table E.2 are not weak; that is, the instruments are sufficiently strongly correlated
with the endogenous regressor yrussia. Similarly, Model 5 where the first stage F-statistic F(1;
61)=7.44 is less than the rule of thumb value 10, is deemed inappropriate. Table E.3 presents the
95% confidence intervals for the coefficients in Models 3 and 6 that are chosen as the best ones
according to their statistical characteristics.
3 The p-value, also called the significance level, is the probability of drawing a statistic at least as adverse to the null hypothesis as the one actually computed in the sample under consideration, assuming the null hypothesis is correct (see Stock and Watson, 2007, Ch. 3).
16
The condition on exogeneity of the instruments is assessed using the overidentifying
restrictions J-test discussed in Appendix B.1. Under the null hypothesis that all instruments are
exogenous, the J-statistic of the test has a χ2m-k distribution, if the errors in (B2, Appendix B.1)
are homoskedastic. The J-statistic has the form J=mF, where F is the homoskedasticity-only F-
statistic testing the hypothesis H0: δ1 = ... = δm = 0 in regression (B2). The hypothesis H0 is the
hypothesis that the coefficients at all the instruments in the regression of the TSLS residuals on
instrumental (and exogenous, if any) variables are zero. 4
For regression (B2) for Models 3 and 6 in Table E.2 we have:
• Model 3. F(4, 59) = 0.00; J = 4F = 0.00, so that the null hypothesis on endogeneity of
instruments is rejected at the significance level of 0% (in other words, the hypothesis on
exogeneity of instruments is accepted with a confidence probability of 1).
• Model 6. F(3, 59) = 0.00; J = 3F = 0.00, so that the null hypothesis on endogeneity of
instruments is rejected at the significance level of 0% (in other words, the hypothesis on
exogeneity of instruments is accepted with a confidence probability of 1).
Thus, the instruments in both Models 3 and 6 above are relevant and are not weak. That
is, the instruments used in these models are indeed valid.
Is Okun’s law stable?
Using rolling regressions, Knotek (2007) shows that Okun’s law for the US economy is
not stable. First, it is sensitive to business cycle periods. Second, Okun’s coefficient that relates
output growth and unemployment changes over time (due to technological progress and increase
in productivity, for example). Following Knotek, we analyze stability of Okun’s coefficient for
the Russian economy. In contrast to Knotek (2007), in addition to estimation of (rolling) Okun’s
coefficients we also determine, similar to other parts of the project, their confidence intervals.
In the analysis, each rolling regression for Russia is estimated using 20 quarterly
observations from 2003:2 to 2010:4. Thus, each estimation window covers 5 years of quarterly
data. The first regression estimates the relationship between the change in the unemployment rate
and the GDP growth rate using a sample from the second quarter of 2003 to the first quarter of
2008. The estimation window then moves forward one quarter in time and the regression is re-
estimated using the data from the third quarter of 2003 to the second quarter of 2008, etc. The
rolling regressions have the form
Δurussia=α·yrussia+β·q2+const. (8)
The parameters in regression (8) are estimated using instrumental variables for the
regressor yrussia (with the variables pcrudeoil, q1 and q3 used as instruments). Note that 4 In Model 6, q2 is an the exogenous regressor.
17
regression (8) is similar to Model 6 of the TSLS regression of changes in the unemployment rate
on the GDP growth rate (see Table E2). Table E4 provides a summary of statistical
characteristics of the rolling regression. The dynamics of the coefficient α in equation (8) for
different windows of the rolling regression is presented in Table E5 and Figure E3.
As one can see from Figure E3 and Table E5, all the estimates of the parameter α in the
rolling regression lie at the intersection of the 95% confidence intervals [∆𝑡1,∆𝑡2 ] for each
estimation window. That is, all the values of α belong to the intersection
⋂ [∆𝑡1,𝑞4_2010𝑡=𝑞1_2008 ∆𝑡2] = [∆𝑚𝑎𝑥1 ,∆𝑚𝑖𝑛2 ]=[-0.0760, -0.0663]
(here ∆𝑚𝑎𝑥1 = max𝑡 ∆𝑡1 ; ∆𝑚𝑖𝑛2 = min𝑡 ∆𝑡2). Since all the confidence intervals [∆𝑡1,∆𝑡2] do intersect,
the regression coefficients αt in the rolling regressions are indistinguishable at the 5%
significance level. We can, therefore, conclude that Okun’s coefficient for Russia has not
undergone (statistically) significant changes in the considered period from the 2nd quarter of
2003 to the 4th quarter of 2010, despite the 2008 global economic and financial crisis.
Using the statistical characteristics of estimates of rolling regressions in Table E3, we
chose Model 6 in the table as the most appropriate description of the statistical relationship
between the change in the unemployment rate and the GDP growth rate in Russia:
Δurussia = 0.005 - 0.0567 yrussia - 0.01 q2 (9) [0.003; 0.007] [-0.079; -0.034] [-0.014; -0.006]
(the parentheses provide the 95% confidence intervals for the coefficients).
According to (9), the stable rate of unemployment (Δurussia = 0) corresponds to the
quarterly GDP growth rate equal to
𝑦𝑟𝑢𝑠𝑠𝑖𝑎 = 0.0050.0567
− 0.010.0567
𝑞2 = 0.088 − 0.176𝑞2.
A similar result is also provided by a model based on a dynamic version of Okun’s law
(see Model 1 of Table 4.2 in Section 4.1.2). The dynamic version of Okun’s law for Russia
contains the current GDP growth rate and the change in the unemployment rate in the previous
period as the variables in the right-hand side of the equation:
Δurussia = 0.00389 - 0.0856 yrussia - 0.4045 Δurussia(-1). (10) [0.0015; 0.006] [-0.107; -0.064] [-0.623; -0.186]
The model is estimated using the variables pcrudeoil, q1, q2 and q3 as the instruments for
yrussia.
Despite some similarities, models (9) and (10) are fundamentally different. Dynamic
model (10) is not as restrictive in terms of timing of the relationship between GDP growth and
changes in the unemployment rate as static model (9), where one considers only
18
contemporaneous correlations between the variables. However, a drawback of model (10) is that
the relationship in it is more difficult to interpret.
In summary, according to estimated Okun’s model (9), on average, a 1% increase in the
quarterly GDP growth rate in Russia is associated with a decrease in the unemployment rate by
0.057% compared to the previous quarter. More precisely, for the 95% confidence level (or, in
other words, with the 95% confidence probability), the latter decrease in the unemployment rate
lies in the interval from 0.034% to 0.079%).
One should note that the Russian Ministry of Economic Development and analogous
government agencies of other CIS countries develop several forecasts of socio-economic
development in the medium and long run. The main economic indicators considered in
forecasting are the economic growth indicators that are used, in part, to construct the forecasts of
social indicators. For example, “The forecast of socio-economic development of the Russian
Federation in 2011 and the planning period of 2012 and 2013”, September 23, 2010, provides
Version 2b of forecasts of the GDP growth rate and the unemployment rate in 2011-2013 (Table
4.3). According to the estimates of the Russian Ministry of Health and Social Development, in
2011-2013, the number of registered unemployed will decrease rather slowly from 2.2 million in
2010 to 1.95 million in 2013. A conservative version of the forecast, the number of registered
unemployed will be larger and become 2.1 million in 2013.5
Table 4.3. GDP growth rates, %
Forecast
2010 2011 2012 2013 GDP growth rate (Version 2b) 4.0 4.2 3.9 4.5
The forecast in the above document is indeed contained in the prediction interval in
Figure D8. However, as discussed above, for the 95% confidence level, the prediction intervals
for the combinations <unemployment rate, GDP growth rate> are rather large.
4.1.3. Further results: Analysis of the relationship between unemployment and
economic growth using the concept of elasticity
In this section, we focus on the analysis of the relationship between the unemployment
rate and GDP growth in Russia using the economic concept of elasticity. The models considered
in the section are somewhat different from those discussed above. Namely, in this section, we
use the level variable of the unemployment rate as the variable in the analysis. This is in contrast
to the previous sections that focused on models involving the changes in the unemployment rate.
5 http://www.economy.gov.ru/minec/activity/sections/macro/prognoz/doc20100923_07
19
We first consider the statistical relationship between the unemployment rate and the
logarithm of Russian GDP. We estimate the regression of the unemployment rate Urussia on the
logarithm of the GDP Yrussia using quarterly data on these variables for the period 2003:1-2010:4
(the sample size n=32) and the instrumental variables (TSLS) method with the instrument given
by the crude oil price Pcrudeoi in US dollars for barrel (see Table 4.4). The estimated regression is
Urussia=0.23693 - 0.01856·lnYrussia (11)
Table 4.4. TSLS regression for the unemployment rate
and the logarithm of GDP in Russia (2003:1 – 2010:4)
Regressors Dependent
variable Urussia
[95% Conf. Interval] Regressors
Dependent variable lnYrussia
[95% Conf. Interval]
(1) (2)
lnYrussia -0.01856** (0.00467) [-0.028, -0.009] Urussia
-53.887** (13.53) [-81.5; -26.2]
const 0.23693** (0.04101) [0.153, 0.321] Const 12.77**
(1.00) [10.7; 14.8]
F(m,n-m-1) F(1, 30) = 15.85 F(m,n-m-1) F( 1, 30) = 15.85 Prob>F 0.0004 Prob>F 0.0004 Instrumental variable Pcrudeoil
Instrumental variable Pcrudeoil
First stage F-statistic F(1,30) = 44.72 First stage F-
statistic F(1,30) = 29.33
Overidentifying restrictions J-test and p-value
0.00 1.00
Overidentifying restrictions J-test and p-value
0.00 1.00
Note: 1) Robust standard errors are given in parentheses under the coefficients; 2) ** denotes significance at 1% level.
Write equation (11) in the general form
U= α+ β lnY. (12)
This implies
𝑌 = 𝑒𝑈−𝛼𝛽 .
Consequently, the coefficient of elasticity of Y with respect to U is given by
𝜀𝑈(𝑌) = 𝑑𝑌𝑑𝑈∙ 𝑈𝑌
= 𝑈𝛽
.
Thus, the coefficient of elasticity of the GDP Y with respect to the unemployment rate U is given
by the ratio of U to β.
For model (11) one has
𝜀𝑈(𝑌) = 𝑈𝛽
= − 𝑈0.01856
= −53.89𝑈.
Consequently,
20
𝜀𝑌(𝑈) = 𝛽𝑈
= −0.01856𝑈
.
The Russian GDP level is elastic with respect to the unemployment rate if
|𝜀𝑈(𝑌)| = 53.89𝑈 > 1,
that is, if U>0.01856. It is inelastic if U<0.01856. The elasticity condition U>0.01856 holds in
Russia in the period 2003:1-2010:4 under consideration. The maximal value of U in the period
2003:1-2010:4 is max U=0.094 (attained in 2009:1) and the minimal value of U in the period is
min U=0.054 (in 2008:2). Therefore, in the period under consideration, the absolute value of the
coefficient of elasticity of GDP with respect to the unemployment rate was in the interval
[2.91; 5.07]. The end of the present section presents a more detailed analysis of (confidence)
intervals for the elasticity coefficient(s).
Thus, from 2003:1 to 2010:4, (the factors affecting output and unemployment in Russia
determined the situation where), a 1% decrease in the unemployment rate was associated with
the GDP growth in the range from 2.9% to 5%. One should note that here the meaning of the
expression “a 1% decrease in the unemployment rate” is somewhat different compared to Okun’s
law (1). 6 Model (1) implies the conclusions where the change in the unemployment rate is 1%.
This means that the number NU of the unemployed and the number NL of the employable
population (the total labor volume) change in such a way that
Ut = 𝑁𝑡𝑈
𝑁𝑡𝐿= 𝑁𝑡−1
𝑈
𝑁𝑡−1𝐿 ∓ 0.01. (13)
In contrast, in this section, the expression “a 1% decrease (increase) in the unemployment
rate” corresponds to the relation
Ut = 𝑁𝑡𝑈
𝑁𝑡𝐿= (1 ∓ 0.01) 𝑁𝑡−1
𝑈
𝑁𝑡−1𝐿 . (14)
It is clear that a 100n% decrease (increase) in the unemployment rate (that is, its
decrease/increase by n shares) in the sense of relation (13) corresponds to its 100𝑛𝑈𝑡−1
% decrease
(increase) in terms of relation (14).
Relation (14) is convenient because it allows one to determine the interval of changes in
the unemployment rate where the coefficient of elasticity of the GDP volume with respect to the
unemployment rate is greater or less than one. The latter conclusions are important because, if
the elasticity coefficient is greater than one, then (the factors in system of equations (2) are such
that) policy measures aimed at reducing the unemployment have an even greater effect in the
sense of the accompanying increase in the economic growth. And conversely, if the above
6 Essentially, since, as discussed above, the analysis and conclusions in this section concern the level variable of the unemployment rate but not its changes, as in Okun’s law.
21
elasticity is less than one, then policy measures aimed at increasing economic growth have an
even greater effect in the sense of the accompanying reduction in the unemployment.
Whatever of the relations, (13) or (14), is used, the concept of unemployment decrease
(increase) is a matter of convention. Indeed, one can decrease the unemployment rate 𝑈𝑡 = 𝑁𝑡𝑈
𝑁𝑡𝐿 in
two ways: either decrease the number NU of the unemployed with the number NL of the
employable population being fixed or increase the total labor force NL with a fixed number of the
unemployed. In general, the concept of the unemployment decrease (increase) is rather abstract
and does not contain much useful economic information without taking into account conditions
that are specific to a country under consideration. These conditions include the total population,
the number of employable people and that of economically active population, technology level,
the country’s aggregate wealth, the method of coordination of economic activity used in the
economy, natural conditions, etc. Generally speaking, theoretically, under any method of
coordination of economic activity, one can decrease the unemployment rate if this is set as a goal
for the society. The question of interest to us is whether this would positively affect economic
growth or have an opposite effect.
The GDP growth rate and the change in the unemployment rate are only two of many
indicators that characterize the economy of a particular country at a particular time period. It
seems impossible to view the relationship between these variables as an economic law for any
market economy. However, it is of interest to explicitly determine or estimate the parameters of
the relationship, albeit a statistical one, between the two indicators. First, cross-country
comparisons of parameters in the model describing the relationship allow one to provide a
comparative analysis of labor markets in different economies. Second, in system (2), both the
variables, the GDP growth rate and unemployment rate, depend on a complex of the same
factors. This means that each of the variables contains information on the value of the other one.
If some conditions lead to a change in one of the variables in the pair <GDP growth,
unemployment rate>, one can hope that they would accordingly change the other indicator in the
pair as well.
Confidence intervals for elasticity using the delta method
This section provides confidence intervals for output and unemployment rate elasticities
constructed using the delta method and the estimates of the relationship between these variables
obtained in Table 4.4. The description of the delta method and its applications to construction the
confidence intervals for the elasticities are provided in Appendix B.2.
Figure 4.1 presents the 95% confidence interval for the coefficient 𝜀𝑌(𝑈) of elasticity of
the unemployment rate with respect to the GDP level in Russia.
22
Thus, with the 95% confidence probability, one can assert that the average values of the
coefficient 𝜀𝑌(𝑈) of elasticity of the unemployment rate with respect to the GDP level in Russia
in the period 2003:1-2010:4 lie in the interval from -0.29 to -0.2 (see Figure 4.1). Similarly, the
average values of the coefficient 𝜀𝑈(𝑌) of elasticity of the Russian GDP level with respect to the
unemployment rate in the period 2003:1-2010:4 lie in the interval from -1.86 to -8.28 (see Figure
4.2).
Figure 4.1. The 95% confidence intervals for the coefficients of elasticity of the unemployment
rate with respect to the GDP level in Russia
Figure 4.2 presents the confidence intervals for the coefficient of elasticity of the Russian
GDP level with respect to the unemployment rate.
Figure 4.2. The 95% confidence intervals for the coefficients of elasticity of the GDP level in
Russia with respect to the unemployment rate
-0,35
-0,25
-0,158 8,5 9 9,5
Ela
stic
ity
log GDP
Elasticity of Unemployment rate with respect to GDP, Russia
-9
-7
-5
-3
-10,05 0,06 0,07 0,08 0,09 0,1
Ela
stic
ity
Unemployment Rate
Elasticity of GDP with respect to Unemployment rate, Russia
23
4.2.Uzbekistan
Data and notation
In Uzbekistan, the economic statistics provided by different government agencies varies
and is often contradictory. In addition, it is usually difficult to receive access to economic
databases of government and other organizations. Here one fully observes the problems
described in Section E.2, including the problems with data. Therefore, below we describe in
more detail the data sources and methods for calculating the indicators used in the estimation of
Okun’s model parameters for Uzbekistan:
Y is the GDP level in national currency according to the State Committee of Uzbekistan
on Statistics;
U is the unemployment rate in shares. The variable U is calculated by the formula
𝑈 = 𝐴−𝐿𝐿
,
where A is the economically active population, thousands of people; L is the total number of
people employed in the economy (labor resources), thousands of people, according to the
Ministry of Labor and Social Security of the Republic of Uzbekistan; 𝑙 = 𝐿−𝐿−1𝐿−1
is the labor
growth rate; and r is the dummy (political) variable that equals zero before 2004 and equals 1
thereafter. The political variable r can be interpreted in two ways. First, since 2004 one observes
a steady increase in migration flow to Russia, with a significant role in the process played by
migrants from Uzbekistan (see also the discussion in Section 4.7). Second, in October 2003, the
Uzbek Government officially announced the national currency convertibility for current
transactions. The government’s decision was, apparently, influenced, in part, by an increase in
transfers from Uzbek citizens working in Russia. One should note that, before 2003, the Uzbek
Central Bank has already made two attempt to liberalize the foreign exchange market (see
Figure E.4). Namely, on May 9, 2000, the Central Bank increased the official exchange rate of
US dollar to Uzbek Soum to the level of its unofficial (market, shadow) exchange rate. As a
result, the official US dollar exchange rate has increased by 1.561 times. The same operation was
conducted on November 1, 2001, when the official US dollar exchange rate was increased by
1.57 times. However, these two attempts of the Central Bank to liberalize the foreign exchange
market and to introduce Uzbek Soum convertibility did not reach the target (see, among others,
the discussion in Ibragimov, Khamidov and Davidova, 2011). Due to the gradual liberalization of
the foreign exchange market since 2004, the official exchange rate of US dollar to Uzbek Soum
was practically no different from the market (shadow) exchange rate. This situation lasted almost
until 2009, when the market exchange rate of the US dollar started to be significantly higher than
its official exchange rate set by the Central Bank. Apparently, this was due to the 2008 world
24
financial crisis when Russia and Kazakhstan introduced measures limiting the labor import from
Uzbekistan and other post-Soviet Central Asian countries. Accordingly, Uzbekistan has
experienced a decline in labor export and in the volume of foreign currency transfers from
abroad. Regardless of what explains the 2004 phenomenon in Uzbekistan, Figure E5 shows that,
starting with 2004, the dynamics of the unemployment rate in the country has acquired
characteristics that are different from those before 2004 and, surprisingly, it has begun to
decrease significantly.
4.2.1. Seasonal components of unemployment and economic growth
Consider the dynamics of the quarterly GDP growth rate yuzbekistan and changes
Δuuzbekistan in the unemployment rate in Uzbekistan (see Figure E6). One can see that, similar
to the case of Russia discussed in Section 4.1.1, the dynamics of these indices is influenced by
seasonal factors.
As in Section 4.1.1, in order to identify the seasonal components, we use the dummy
variables q1, q2 and q3, that correspond to the quarters of a year. The results of estimation of the
regression of the variables Δuuzbekistan and yuzbekistan on the variables q1, q2 and q3 are
provided in Table E11.
According to the results in Table E6, with a significance level of 0.05, one can indicate
that, ceteris paribus, compared to the fourth quarter of a year under consideration, the change in
the unemployment rate in Uzbekistan in the first quarter is greater by 3 to 4 percentage points; in
the second quarter it is smaller by 1 to 2%; and in the third quarter the change in the
unemployment is smaller by 0.7 to 2%. Similarly, compared to the fourth quarter of a year under
consideration, the GDP growth rate in Uzbekistan in the first quarter is smaller by 47.7 to 57.4
percentage points; in the second quarter it is greater by 14 to 25.8%; and in the third quarter the
GDP growth rate is greater by 16.8 to 34.7%.
4.2.2. Estimates of Okun’s model
Consider the change in the unemployment rate Δuuzbekistan as the dependent variable.
We use the variable yuzbekistan as the regressor in the model for Δuuzbekistan. Table E7
provides the results of the TSLS estimation for the regression model using the instrumental
variables l, q1 and q3 for yuzbekistan. As discussed in the previous section, the variables q1 and
q3 represent the seasonal factor in the rate of economic growth. The choice of the variable l that
characterizes the change in labor resources as an instrumental variable for the regressor
yuzbekistan is also natural.
Note that although the standard errors in Models 1 and 2 of Table E7 take into account
the possible heterogeneity of variables, they do not account for possible autocorrelation of
25
regression errors over time. Therefore, the models require an additional test for autocorrelation
of the errors over time. The test is not needed in Model 3 of Table E7 that contains the lags of the
variable Δuuzbekistan.
As discussed in Appendix B.1, validity of instruments is verified similar to Section 4.1.2
for Russia.
According to the estimation results, Okun’s law for Uzbekistan can be summarized as
follows:
• According to the Model 1 of Table E7, on average, a 1% increase in the quarterly GDP
growth rate in Uzbekistan is associated with a decrease in the unemployment rate by 0.066%
compared to the previous quarter (more precisely, with the 95% confidence probability, the
latter decrease in the unemployment rate lies in the interval from 0.056 to 0.077%):
Δuuzbekistan=0.0058 – 0.0663yuzbekistan.
• According to Model 2, on average, a 1% increase in the quarterly GDP growth rate in
Uzbekistan is associated with a decrease in the unemployment rate by 0.067% compared to
the previous quarter (more precisely, with the 95% confidence probability, the decrease is
between 0.057 to 0.076%). The model includes the political dummy variable r (the indicator
of the effects of 2004):
Δuuzbekistan=0.0078 – 0.0666yuzbekistan – 0.0043r.
• Model 3 contains the lags of changes in the unemployment rate and the political dummy for
2004:
Δuuzbekistant=0.007 – 0.066yuzbekistant – 0.2Δuuzbekistant-1 – 0.0045r.
4.3. Ukraine
The variable Δuukraine is the dependent variable in the analysis. Table A8 contains the
results of the TSLS estimation of the regression for Δuukraine using the instrumental variables
yrussia, pcotton, q2, q3 and q4 for the regressor yukraine. Verification of the relevance and
exogeneity of the instrumental variables is conducted similar to Appendix B.1 and the above
discussion for Russia and Uzbekistan. For instance, Model 1 in Table E8 is inappropriate since
the first stage F-statistic F(2, 25) = 9.7 is less than 10. We chose Models 2 and 6 as the best ones
according to their statistical characteristics. Table E9 provides the 95% confidence intervals for
these models.
Okun’s law to Ukraine may be summarized as follows:
• According to Model 2 in Table E14, on average, a 1% increase in the quarterly GDP growth
rate in Ukraine is associated with a decrease in the unemployment rate by 0.05% compared to
26
the previous quarter (more precisely, with the 95% confidence probability, the latter decrease
in the unemployment rate lies in the interval from 0.015 to 0.084 percent). Other things being
equal, the unemployment rate in the second quarter of a year under consideration, is smaller
by 0.002% compared to the other quarters (more precisely, it is smaller by 0 to 0.006 percent
with the 95% confidence probability).
• According to Model 6 in the table, on average, a 1% increase in the quarterly GDP growth
rate in Ukraine is associated with a decrease in the unemployment rate by 0.051% compared
to the previous quarter (more precisely, the unemployment decrease is between 0.025 to
0.078% for the 95% confidence probability).
4.4. Belarus
The indicator Δubelarus is the dependent variable in the analysis in this section. Table
E10 contains the results of the TSLS using yrussia and pgold as the instruments for the regressor
ybelarus.
Okun’s law for Belarus may be formulated as follows.
On average, a 1% increase in the GDP quarterly growth rate in Belarus is associated with
a decrease in the unemployment rate in this country by 0.00567% compared to the previous
quarter (more precisely, the unemployment rate decrease belongs to the interval from 0.0024 to
0.0089 percent with the 95% confidence probability).
4.5. Moldova
Consider Δumoldova as the dependent variable. Table A11 contains the results of TSLS
estimation that uses the variables y2usa, q2 and q3 as the instruments for the regressor ymoldova.
Similar to the discussion in Section 4.2.2, although the standard errors in Models 1 and 2
in Table E16 are robust to heterogeneity in the variable, they do not account for possible
autocorrelation of the regression errors over time. This requires an additional test for
autocorrelation in the errors. The possible autocorrelation of the errors is taken into account in
Models 3 and 4 by the use of robust standard errors for the coefficients.
Okun’s law for Moldova can be described as follows:
• According to Model 1, on average, a 1% increase in the quarterly GDP growth rate in
Moldova is associated with a decrease in the unemployment rate by 0.05% compared to the
previous quarter (more precisely, the latter decrease in the unemployment rate ranges from
0.015 to 0.081 percent with the 95% confidence probability). In addition, other things being
equal, the unemployment rate is greater by 0.02% in the first quarter of a year considered in
comparison with its other quarters (more precisely, it is greater by 0.004 to 0.041 percent
with the 95% confidence probability).
27
• According to Model 2, on average, a 1% increase in the quarterly GDP growth rate in
Moldova is associated with a decrease in the unemployment rate by 0.078% compared to the
previous quarter (more precisely, the unemployment decrease with respect to the previous
quarter is between 0.037 to 0.12 percent with the 95% confidence probability).
• Models 3 and 4 incorporate the one-period lag of the change in the unemployment rate and
(as an additional instrumental variable) that of the GDP growth rate. The estimates of these
models are the following:
Model 3:
Δumoldovat = 0.00336 - 0.0596 ymoldovat - 0.35 Δumoldovat-1.
Model 4:
Δumoldovat = -0.00125 - 0.046 ymoldovat - 0.39 Δumoldovat-1 +0.015 q1.
The instruments for ymoldova in these models are given by ymoldova(-1), q2, q3 and
y2usa.
4.6. Kazakhstan
We consider Δukazakhstan as the dependent variable. Table E12 contains the results of
the TSLS using the instruments pcrudeoil, q1 and q3 for the regressor ykazakhstan.
Similar to the analysis in Section 4.1.2 for Russia, we analyze stability of Okun’s
coefficient for Kazakhstan’s economy and also construct the confidence intervals for the
coefficient using rolling regressions.
Each rolling regression for Kazakhstan is estimated using 20 quarterly observations from
the 2nd quarter of 2003 to the 3rd quarter of 2011. Thus, each rolling window contains 5 years of
quarterly observations. Figure E.7 represents the graphs of the rolling regressions for the
coefficient α in the equation
Δukazakhstan=α·ykazakhstan+β·q2+const.
As is seen from Figure E7 and Table E13, all the estimates of the coefficient α obtained
using the rolling regressions lie in the intersection of the 95% confidence intervals [∆𝑡1,∆𝑡2].
That is, all the estimates of α belong to the set ⋂ [∆𝑡1,𝑞4_2010𝑡=𝑞1_2008 ∆𝑡2] = [∆𝑚𝑎𝑥1 ,∆𝑚𝑖𝑛2 ] . (Here
∆𝑚𝑎𝑥1 = max𝑡 ∆𝑡1 ; ∆𝑚𝑖𝑛2 = min𝑡 ∆𝑡2). Since the above intersection is nonempty, similar to the
discussion in Section 4.1.2 for Russia, we conclude that the regression coefficients αt in the
rolling regressions are indistinguishable at the 5% significance level. This further leads to the
conclusion that, similar to the case of Russia, Okun’s coefficient in Kazakhstan has not
undergone (statistically) significant changes in the period from the 2nd quarter of 2003 to the 3rd
quarter of 2011 under consideration.
28
4.7. Cross-country comparative analysis
For comparison of the mechanism of Okun’s law in different countries, consider Table
4.5 and Figures 4.3-4.6. The statistical characteristics of regressions in Table 4.5 are provided in
the corresponding tables in Appendix E.
Table 4.5. Okun’s models
(Δu is the change in the unemployment rate and y is the GDP growth rate)
Country Okun’s model Δu = α – βy Belarus Δu = -0.0004 - 0.0057y Kazakhstan Δu = -0.00084 - 0.0073y Moldova Δu = 0.0029 - 0.05936y Russia Δu = 0.00336 - 0.0747y Uzbekistan Δu = 0.0058 - 0.0663y Uzkraine Δu = 0.0032 - 0.05119y
Figure 4.3. Graphs and the 95% confidence intervals for regressions of the change in the
unemployment rate on the GDP growth rate in Belarus and Kazakhstan
29
Figure 4.4. Graphs and the 95% confidence intervals for regressions of the change in the
unemployment rate on the GDP growth rate in Moldova, Russia, Ukraine and Uzbekistan
Figure 4.5. Graphs of the regressions of the change in the unemployment rate on the GDP
growth rate in Belarus, Kazakhstan, Moldova, Russia, Ukraine and Uzbekistan
-0,015
-0,01
-0,005
0
0,005
0,01
0,015
0,02
0,025
-0,2 -0,15 -0,1 -0,05 0 0,05 0,1 0,15 0,2
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Confidence Interval
RussiaRussiaUzbekistanUzbekistanUkraineUkraineMoldovaMoldova
-0,015
-0,01
-0,005
1E-17
0,005
0,01
0,015
0,02
-0,2 -0,1 0 0,1 0,2
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
RussiaUzbekistanUkraineBelarusMoldovaKazakhstan
30
Figure 4.6. 95% confidence intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Moldova, Russia, Ukraine and Uzbekistan
1. The smallest variability of the unemployment rate with respect to the GDP growth rate, as
measured by Okun’s coefficient, is observed in Belarus (minus 0.0057%) and Kazakhstan
(minus 0.0073%). Apparently, when the output falls in Belarus and Kazakhstan, the freed
labor resources find jobs abroad, mostly in Russia. This is stimulated by the economic union
of Russia, Belarus and Kazakhstan. Besides, the large labor resource market in neighboring
Uzbekistan allows Kazakhstan to use labor migration from that country (including the illegal
one) as a source of cheap labor. As discussed in Section E.2, illegal labor migration is not
accounted for by statistical agencies in the country in estimation of the number of
economically active population and that of the unemployment rate. Apparently, this may
explain very small changes in the unemployment rate in Kazakhstan following the output
changes in this country.
2. The intersection of the 95% confidence intervals for the regressions of the change in the
unemployment rate on the GDP growth rate in Belarus and Kazakhstan are non-empty (see
Figure 4.3). This means that Okun’s models for Belarus and Kazakhstan are statistically
indistinguishable at the 5% significance level.
3. Similarly, the intersection of the 95% confidence intervals for the corresponding regressions
for Moldova, Russia, Ukraine and Uzbekistan is nonempty for the changes of the GDP
-0,015
-0,01
-0,005
0
0,005
0,01
0,015
0,02
0,025
-0,2 -0,15 -0,1 -0,05 0 0,05 0,1 0,15 0,2
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Confidence Interval
RussiaUzbekistanUkraineMoldova
31
growth rate in the interval from -20% to 20% (see Figure 4.6). This means that Okun’s
models for these countries are also statistically indistinguishable at the 5% significance level.
Labor migration and transfers from labor migrants working abroad play a significant role
in budgets of CIS countries (see also Sections B and E.4.2). The main part of these transfers is
sent from Russia into other CIS countries, mainly to Uzbekistan, Ukraine, Tajikistan, Armenia,
Georgia, Azerbaijan, Moldova and Kyrgyzstan. The flow of transfers from Kazakhstan into other
post-Soviet Central Asian countries is also significant (see Yakusheva, 2011). According to
Yakusheva’s (2011) calculations, “in 2007, the volume of transfers from abroad was 49% of the
GDP in Tajikistan, 29% of the GDP in Moldova and 27% of the GDP in Kyrgyzstan”. According
to the estimates by Reznikova (2012), remittances from labor migrants working abroad constitute
4-5% of the Ukraine’s GDP. The number of labor migrants from Ukraine is 3-4 million people,
with about a half of them working in Russia. The number of Uzbek citizens working abroad is
about 800 thousand people, about 4 out of 5 of which work in Russia. The volume of transfers
from labor migrants abroad to Uzbekistan is estimated to be not less than 4% of the GDP of this
country (see Reznikova, 2012). This is likely to be a very low estimate of the transfer volume.
The absolute volume of labor migrants’ remittances significantly exceeds the volume of direct
foreign investment into Uzbekistan. According to estimates in Denisenko (2010, Table 25), at the
end of the 2000s, the number of labor migrants from Uzbekistan was 1600 (1200 – 1700)
thousand people. The volume of migrants’ remittances to Uzbekistan was 18.7% of the GDP in
2008 and 11.5% of the GDP in 2009 (Denisenko, 2010, Table 19). According to the estimates by
the CII-EDB (2012, Figure 3), the number of Uzbek citizens working in Russia was 650-680
thousand of people in 2008-2009. The number has decreased to 500 thousand of people in 2010.
Transfers from abroad play the role of a stabilizing buffer in the economies of CIS
countries exporting labor resources. At the same, the economies of Russia and Kazakhstan are
the main importers of labor resources on the post-Soviet space and are dependent on labor
migrants from other CIS countries. The economic growth in Russia and Kazakhstan led by
petrodollars continues to attract the low and medium qualification workers from the post-Soviet
countries of Central Asia and the Caucasus that have a surplus of labor resources and
significantly lower wages compared to Russia and Kazakhstan.
F. Conclusion
Okun’s law is a concept that postulates a correlation between the decrease in the
unemployment rate and the increase in the GDP growth rate. This relationship is determined by
32
common factors affecting both the rise in output and the fall in unemployment through an
increase in demand for labor.
Some of the main conclusions from the study concern stability of Okun’s relationships
over time, their practical use for evaluation of average effects of economic growth on the
unemployment rate, and vice versa, importance of accounting for statistical errors and
confidence intervals for Okun’s coefficients in applications of Okun’s models and the potential
value of the models for policy decisions and economic forecasting.
• First, the results obtained in the study indicate that Okun’s law and its analogues provide
useful statistical linear models describing the average effects of economic growth on
changes in the unemployment, and vice versa. The statistical relationships between the
variables given by Okun’s models can be applied, for instance, for practical evaluation of the
magnitude of average changes in the unemployment rate following an observed (or given)
increase (decrease) in the GDP growth rate in a country.
For instance, according to the estimates of Okun’s model for Russia obtained in the
project, on average, a 1% increase in the quarterly GDP growth rate in this country is
associated with a decrease in the unemployment rate by 0.06% compared to the previous
quarter (more precisely, with the 95% confidence probability, the latter average percent
decrease in the unemployment rate, Okun’s coefficient, lies in the interval from 0.03 to 0.08).
Similarly, in Ukraine, the average effect of a 1% increase in economic growth on the change
in the unemployment rate is 0.05%. The smallest average variability of the unemployment
rate with respect to the GDP growth rate, as measured by Okun’s coefficient, is observed in
Belarus (minus 0.0057%) and Kazakhstan (minus 0.0073%).
• Second, our results point out to stability over time for Okun’s law and its modifications that
describe the average relationship between economic growth and unemployment. For
instance, according to estimates using quarterly data and rolling regressions for 2003-2009 in
Russia, Okun’s coefficients for this country at different time periods are statistically
indistinguishable at the 5% significance level. The same situation holds for Okun’s
coefficients in Kazakhstan for the period from 2003 to 2011. These conclusions point out to
stability of the coefficients and Okun’s law in these countries in the above periods. They
further emphasize importance of accounting for statistical errors and confidence intervals of
point estimates of Okun’s coefficients in the analysis of development of labor markets and
their changes over time.
• A related conclusion concerns importance of taking into account statistical errors of point
estimates of Okun’s coefficients in cross-country comparisons of labor markets. For instance,
the cross-country comparisons using confidence intervals for Okun’s coefficients indicate
33
that Okun’s models for Belarus and Kazakhstan are statistically indistinguishable (e.g., at the
5% significance level). Similarly, the models for Russia, Moldova, Ukraine and Uzbekistan
are statistically indistinguishable as well. This, in particular, points out to similarities and/or
interconnectedness of labor markets in these groups of countries (see the discussion in
Section E.4.7).
• Third, one of key conclusions of the study is the need to emphasize the care that should be
taken in applications of simple rules of thumb like Okun’s law for average effects of
economic growth on unemployment. This concerns, in the first place, unreliability of the use
of Okun’s models for economic forecasting and unambiguous policy conclusions using only
point estimates of Okun’s coefficients.
For instance, according to regression confidence intervals for Okun’s models
obtained in the study, for a wide range of changes in Russian GDP growth rate, the
corresponding average values of changes in the unemployment rate in Russia are statistically
indistinguishable at the 5% significance level. That is, with the significance level (probability
of error) of 5% (or less), one cannot assert that the average values of changes in the
unemployment rate are different from each other, even if they correspond to (very) different
GDP growth rates.
The situation is even worse for forecasting changes in the unemployment rate in
Russia. According to the results in the project, for a very wide range of changes in the GDP
growth rate (as wide as from -20% to 20%), the 95% prediction intervals for corresponding
changes in the unemployment rate intersect. This means that one cannot econometrically
justify the unemployment rate forecasting using only Okun’s law and the GDP growth rates.
More precisely, the prediction intervals for the regression of the change in the
unemployment rate on the GDP growth rate are so large that it makes it impossible to
forecast the change in unemployment that corresponds to a given value of the GDP growth
rate using only Okun’s hypothesis (model). According to the results in this paper, even the
95% confidence intervals for the regressions of changes in the unemployment rate on the
GDP growth rate are such that, in many cases, it is impossible to make conclusions on
significant differences in Okun’s coefficients at the 5% level. Therefore, the conclusions on
the values of Okun’s coefficient have the confidence level much less than 95% and even less
than 90%. The value of economic conclusions with such small confidence level for policy
decisions or forecasting is rather low.
• The most important contribution and conclusion of our study is the emphasis on the necessity
of the use of econometrically and statistically justified inference methods and that of
accounting for statistical errors of estimates obtained. This is especially important in the case
34
of such simple rules of thumb as Okun’s law that are tempting to use for unambiguous policy
decisions and economic forecasts, as well as for unambiguous comparisons across countries
and convenient summaries of economic development over time.
The analysis in the project emphasizes that such econometrically justified approaches
as instrumental variables methods are necessary for valid inference on and correct estimation
of economic models under possible endogeneity problems that very often arise in practice. In
addition, it is important that economic policy decisions take into account possible statistical
errors of the obtained estimates for economic models dealt with. The decisions should be
based not just on point estimates of the model parameters but also take into account their
standard errors and confidence intervals. The study makes it clear that a failure to use
econometrically justified inference methods or to account for errors or statistical problems in
the estimates obtained may lead to wrong statistical (and, potentially, policy) decisions and to
conclusions that may be far from reality.
• In addition to Okun’s models, the study further focuses on the analysis of the relation
between unemployment and GDP growth using the economic concept of elasticity. To our
knowledge, despite existence of examples of simple arithmetic calculations of such
elasticities in the literature using, e.g., only two observations on each of the above two
variables at the beginning and the end of periods of interest, rigorous econometric studies and
applications of the elasticity analysis to the above problem have not yet been considered in
previous works. The paper shows that the elasticity analysis, with its well-known
interpretation in terms of the effects of percent changes in one of the variables considered on
percent changes in the other, provides useful conclusions that complement those obtained
using estimates of Okun’s models. In addition, naturally, the elasticity coefficients of
unemployment with respect to output, and vice versa, are estimated using regressions with
logs of the variables considered. The latter regressions provide useful complementary
alternatives to the standard Okun’s regressions that may be used, in particular, in the
assessment of reliability of conclusions implied by Okun’s law. The report provides both
point estimates of elasticity coefficients for unemployment and economic growth and also,
similar to the rest of the analysis, confidence intervals for them (see Section Е.4.1.3).
The use of the elasticity concept allows one to determine, for each country under
consideration, the ranges of unemployment rates for which the GDP is elastic with respect to
unemployment (that is, the coefficient of elasticity of GDP with respect to the unemployment
rate is greater than one) and those for which it is inelastic (the elasticity coefficient is less
than one).
35
The latter conclusions are important because, as discussed in the report, if the
elasticity coefficient is greater than one, then policy measures aimed at reducing the
unemployment have an even greater accompanying effect in the sense of increasing
economic growth. And conversely, if the above elasticity is less than one, then policy
measures aimed at increasing economic growth have an even greater accompanying effect in
the sense of unemployment reduction.
• One should note that the study provides several economic and econometric arguments for
validity of instrumental variables used in the analysis, including the arguments for their
relevance and exogeneity.
In particular, one should emphasize the role of seasonality as a variable that is strongly
correlated with endogenous regressors in Okun’s models and their analogues. This points out
to validity of its use as an instrument in the IV analysis. The above correlation has a natural
economic explanation similar to the case of the use of rainfall and weather as instruments in
estimation of demand and supply functions in the very first classical example of an
application of the instrumental variable methods by Philip Wright (Wright, 1928; see, for
instance, the discussion in Ch. 12 in Stock and Watson, 2007). As discussed in the study on
the project, both the GDP growth rates and changes in the unemployment rate in CIS
countries are characterized by strong seasonality (see Section E.4). Apparently, this may be
explained by severe climate conditions in the Russian Federation and by strong influence of
the conditions on the Russian labor market on the labor markets in other CIS countries.
Similarly, as discussed above and throughout the report (see, for instance, Sections B,
E.4.2 and E.4.7), the labor markets in most of the CIS countries are, naturally, strongly
interconnected and significantly affected by labor migration, mostly to Russia (and, in the
case of post-Soviet Central Asian economies, also to Kazakhstan). Moreover, the economic
conditions and growth in a number of CIS countries are strongly affected by the flow of
remittances and transfers from migrants working abroad, mostly in Russia, that constitute a
significant share of the countries’ GDP (see the discussion in the above sections and
throughout the report). In addition, as discussed in a number of works (see, among others, the
discussion in Section C and references therein), the labor markets in most of the CIS
countries operate to a large extent in a way very similar to the Russian labor market.
The strong influence of economic conditions and migration policy in Russia on the
labor markets in other CIS countries and the above similarity in the modus operandi of the
post-Soviet labor markets motivates the use of the GDP growth rates and other economic
indicators for Russia as instrumental variables for economic growth in other CIS economies
in the analysis of Okun’s models. A large volume of international trade and influence of the
36
conditions on the world foreign exchange and other markets on the CIS economies further
motivates the use of such instrumental variables as, for instance, GDP growth in the US and
China in the study.
Concerning the exogeneity condition for the instrumental variables used in the analysis, one
should note that a number of studies in the literature emphasize relatively stable or, more
precisely, highly inertial or “sticky” (un)employment as one of the main long-term distinctive
features of the labor market in Russia and most of the CIS countries (see the discussion in
Section C and references therein).
Inflexibility of (un)employment in Russia with its little immediate response to
changes in economic conditions and external shocks further motivates the use of IV methods.
In particular, it suggests that the exogeneity condition is likely to be satisfied for many
potential instruments, like those discussed above as well as for such variables as lags of GDP
growth rates that are also used in the study. In addition, the economic factors behind the
modus operandi of the Russian labor market discussed above also help to motivate and
explain exogeneity for the potential instrumental variables.
We emphasize that the analysis on the project discusses in detail the methods and results on
rigorous formal econometric tests for validity of all the instruments used, such as those on the
TSLS first stage F-statistics for testing instrument relevance and on the overidentifying
restrictions J-test of instrument exogeneity. The economic arguments and formal
econometric tests allow us to determine, for each of the CIS countries under consideration,
Okun-type models that are the most appropriate according to their statistical characteristics
and economic motivation.
Some suggestions for further research
• The analysis in the project focuses on six CIS countries: Belarus, Kazakhstan, Moldova,
Russia, Ukraine and Uzbekistan. Since, as discussed above, Okun’s models for Belarus and
Kazakhstan and those for Russia, Moldova, Ukraine and Uzbekistan are statistically
indistinguishable, it would be interesting to construct two separate aggregate Okun’s models
using the data for all countries in these two groups. The approach would, in particular, allow
one to use larger samples of data than in the case of individual Okun’s laws for each
economy. Compared to the individual Okun’s regressions for each country, this would lead
to more reliable estimates of the parameters in (aggregate and thus averaged) Okun’s models.
The latter averaged models, however, would be based on combined data samples. Their
parameters would thus describe the effects of economic growth on changes in the
37
unemployment rate that hold on average for each of the groups considered, in contrast to
individual Okun’s models that characterize the average effects for each country.
• In addition, the inference methods and approaches used in the study are applicable in the case
of other economies. An interesting and important problem that is left for further research is to
explore their applications in the case of other transition and developed countries, including
other post-Soviet economies. A related problem, mostly left for further analysis, consists in a
wide-scale comparison of the results obtained for Russia and other CIS countries with those
available in the literature for transition and developed economies and the implied assessment
of reliability of findings in previous studies on the topic.
More generally, the use of econometrically justified inference methods like instrumental
variable estimation approaches is in fact necessary in the case of possible deviations from the
standard assumptions of the commonly used OLS, such as regressor endogeneity problems. The
areas for applications of instrumental variable methods explored in the literature include
estimation of demand and supply functions, inference on the Phillips curve and many others.
Most of works on these applications focus on the case of developed markets. We hope that
instrumental variable methods considered in the study, together with other econometrically
justified and robust methods, will also make their way to become standard tools of the analysis
for transition economies.
G. Bibliography
Akhundova, O. V., Korovkin, A. G. and Korolev, I. B. (2005). The relationship between
the dynamics of GDP and unemployment: Theoretical and practical analysis. Proceedings of the
Institute for Economic Forecasting, Russian Academy of Sciences (I. B. Korovkin, Ed.). MAKS-
Press, Moscow (in Russian). http://www.ecfor.ru/pdf.php?id=books/kor03/02
Anatolyev, S. (2007). Optimal instruments. Quantile, 2, 61-69. http://quantile.ru/02/02-
SA.pdf
Arabaci, R. Y., Arabaci, O. (2010), Asymmetries in Okun’s Law: evidence from Turkey,
IREC 2010 – Workshop 1, http://www.fafo.no/irec/workshop1.html
Ball, L., Leigh, D. and Loungani, P. (2012). Okun’s Law: Fit at 50? Paper presented at
the 13 th Jacques Polak Annual Research Conference, Hosted by the IMF, Washington, DC –
November 8-9, 2012. http://www.imf.org/external/np/res/seminars/2012/arc/pdf/BLL.pdf
Barro, R. J. and Sala-i Martin, X. (2004). Economic Growth. MIT Press, Cambridge,
MA.
38
Boeri, T. and Terrell, K. (2002). Institutional determinants of labor reallocation in
transition. Journal of Economic Perspectives 16, 51-76.
CII-EDB (2012). Labor migration in the Single Economic Space: Analysis of the
economic effect and institutional and legal consequences of ratification of the agreements on
labor migration. Report 3, Center for Integration Studies, European Development Bank.
http://www.eabr.org/general//upload/reports/migration-report.pdf
Commander, S. and Tolstopyatenko, A. (1997). Unemployment, restructuring and the
pace of transition. In: Lessons from the Economic Transition. Central and Eastern Europe in the
1990s (S. Zecchini, Ed.). Kluwer Academic Publishers, Dordrecht.
Denisenko, М. (2010). Migration and remittances in Central Asia and South Caucasia.
Economic and social commission for Asia and the Pacific. Expert Group Meeting on
Strengthening Capacities for Migration Management in Central Asia, 20 and 21 September
2010, Bangkok.
Draper, N.R., Smith, H. (1981). Applied Regression Analysis. Second Edition. John
Wiley and Sons, New York.
Ebbes, P. (2007). A non-technical guide to instrumental variables and regressor-error
dependencies. Quantile 2, 3-20. http://quantile.ru/02/02-PE.pdf
Gabrisch, H. and Buscher, H. (2006), The relationship between unemployment and
output in post-communist countries. Post-Communist Economies, 18, 261 – 276.
Gimpelson, V. E. and Kapeliushnikov, R. I. (2005). Non-standard employment and
Russian labor market. Preprint WP3/2005/05, Series WP3, The Problems of Labor Market,
Higher School of Economics, Moscow (in Russian).
Gimpelson, V. E. and Kapeliushnikov, R. I. (2008). Wage in Russia: Evolution and
Differentiation. Higher School of Economics, Moscow (in Russian).
Gimpelson, V. E. and Kapeliushnikov, R. (2011). Labor market adjustment: Is Russia
different? IZA Discussion Paper No. 5588. http://www.eerc.ru/article_admin?page=3
Gimpelson, V. E., Kapeliushnikov, R. I. and Lukyanov, A. L. (2010). Education level of
Russian employees: Optimal, excessive or inadequate? Preprint WP3/2010/09, Серия WP3, The
Problems of Labor Market, Higher School of Economics, Moscow (in Russian).
Gordon, R. J. (1984). Unemployment and potential output in the 1980’s. Brookings
Papers Econom. Activity 15, 537–564.
Harris, R. and Silverstone, B. (2001). Testing for asymmetry in Okun's law: A
cross−country comparison. Economics Bulletin 5, 1−13.
39
Howitt, P. and Weil, D. N. (2008). Economic growth. In: The New Palgrave Dictionary
of Economics, 2nd Edition (S. N. Durlauf and L. E. Blume, Eds.). Palgrave Macmillan, New
York.
Ibragimov, M. and Ibragimov, R. (2010). Measurement of Economic Progress. In: the
International Encyclopedia of Statistical Science (M. Lovric, Ed.). Springer, New York.
http://onlinelibrary.wiley.com/book/10.1002/0471667196
Ibragimov, M., Khamidov, R. and Davidova, Z. (2011). Heavy-tailedness and volatility
in emerging foreign exchange markets: Theory and empirics. EERC working paper No. 10/06E.
http://eerc.ru/paperinfo/303
Ibragimov, R. and Müller, U. K. (2010). t-statistic based correlation and heterogeneity
robust inference. Journal of Business and Economic Statistics 28, 453-468.
IMF (2010). Unemployment dynamics during recessions and recoveries: Okun’s law and
beyond. World Economic Outlook April 2010: Rebalancing Growth, Ch. 3, 69-107.
Izyumov, A. and Vahaly, J. (2002). The unemployment - output tradeoff in transition
economies: Does Okun’s law apply? Economics of Planning 35, 317–331.
Kaufman, R. T. (1988), An international comparison of Okun’s Law. Journal of
Comparative Economics 12, 182–203.
Knoester, A. (1986). Okun’s law revisited. Weltwirtschafliches Archiv 122, 4:657–666.
Knotek, E. (2007). How useful is Okun's law? Federal Reserve Bank of Kansas City
Economic Review, Fourth Quarter, 73-103.
http://www.kc.frb.org/publicat/econrev/PDF/4q07Knotek.pdf
Kulekeev, Z. A. (1997). Shadow economy in Kazakhstan: Causes of its appearance and
consequences for macroeconomic stabilization. Kazakhstan Economy, 2, 76-83 (in Russian).
Layard, R. and Richter, A. (1995). Labour market adjustment: The Russian way. In:
Russian Economic Reform at Risk (A. Aslund, Ed.). Pinter, London, 119-148
Moosa, I. A. (1997). A cross-country comparison of Okun’s coefficient. Journal of
Comparative Economics 24, 335-356.
Okun, A. M. (1962). Potential GNP: Its measurement and significance. American
Statistical Association, Proceedings of the Business and Economics Statistics Section, 98-104.
Orlov, A. I. (2002). Econometrics. Examen, Moscow (in Russian).
http://www.aup.ru/books/m153/10_2.htm
Pagan, A. (2007). Weak instruments. Quantile, 2, 71-81. http://quantile.ru/02/02-AP.pdf
Pollock, S. (2007). Estimation of Structural Econometric Equations. Quantile, 2, 49-59.
http://quantile.ru/02/02-SP.pdf
40
Prachowny, M. F. J. (1993). Okun’s law: Theoretical foundations and revised estimates.
Review of Economics and Statistics 75, 331–336.
Reznikova, O. (2012). Perspectives of migration on the post-Soviet space. Institute of the
World Economy and International Relations, Russian Academy of Sciences.
Schneider, F. and Enste, D. (2002). Hiding in the shadows. The Growth of the
Underground Economy, IMF. http://www.imf.org/external/pubs/ft/issues/issues30/index.htm
Sims, C. A. (2007). Thinking about instrumental variables. Quantile, 2, 83-94.
http://quantile.ru/02/02-CS.pdf
Smith, G. (1975). Okun’s Law Revisited. Quarterly Review of Economics and Business
15, 37–54.
Soltwedel, R., Dohse, D. and Krieger-Boden, C. (2000). European labor markets and
EMU challenges ahead. Finance and Development, IMF 37, No. 2.
Steckel, R. H. (2008). Standards of living (historical trends). In: The New Palgrave
Dictionary of Economics, 2nd Edition (S. N. Durlauf and L. E. Blume, Eds.). Palgrave
Macmillan, New York.
Stock J. H., Watson M. W. (2007). Introduction to Econometrics. 2nd Edition. Addison
Wesley, New York.
Tsyplakov, A. (2007). A guide to the world of instrumental variables. Quantile, 2, 21-47.
http://quantile.ru/02/02-AT.pdf
Weber, C. E. (1995). Cyclical output, cyclical unemployment, and Okun’s coefficient: A
new approach. Journal of Applied Economics 10, 433–458.
Wright, P. G. (1928). The Tariff on Animal and Vegetable Oils. Macmillan, New York.
Yakovleva, A. V. (2008). Econometrics. Lecture Notes.
Yakusheva, A. E. (2010). Labor migrants’ remittances as a channel for retranslation of
the world economic crisis on the post-Soviet space. In: Crisis Phenomena in the World Economy
and Politics (World Development, Issue 6; F. G. Vojtolovskiy and A. V. Kuznetsov, Eds.).
Institute of the World Economy and International Relations, Russian Academy of Sciences
(IMEMO RAN), Moscow, pp. 81-87 (in Russian).
Zakhs, S. (1972). The Theory of Statistical Inference. John Wiley and Sons, New York.
41
Appendix A. Data and notation
Initial designation:
Y - GDP in national currency;
U - unemployment rate in fractions;
𝑦 = 𝑌−𝑌−1𝑌−1
– GDP growth in the shares;
Δu=U – U-1 – change in the unemployment rate;
Luzbekistan – the number of employed in the economy of Uzbekistan, in thousands. Source:
Ministry of Labor and Social Protection of the Republic of Uzbekistan.
CPI - Commodity Price Index. 2005=1. Source: IndexMundi
http://www.indexmundi.com/commodities/?commodity=commodity-price-index&months=360
Y1USA – US GDP in billions of dollars at current prices. Source: US Bureau of Economic
Analysis, http://www.bea.gov/
Y2USA – US GDP in billions of dollars in 2005 prices Source: US Bureau of Economic Analysis,
http://www.bea.gov/
YChina – China’s GDP by expenditure, in millions Macau Pataca (MOP) at current prices. Source:
China National Bureau of Statistics, http://www.stats.gov.cn
Pcotton – the price of cotton, US cents per pound. Source: IndexMundi,
http://www.indexmundi.com/commodities/?commodity=cotton&months=360
Pgold – sample price of gold 99.5 US dollars per troy ounce. Source: IndexMundi
http://www.indexmundi.com/commodities/?commodity=gold&months=360
Psilver – the price of silver in the sample 99.9 US cents per troy ounce. Source: IndexMundi
http://www.indexmundi.com/commodities/?commodity=silver&months=240
Pcrudeoil – the price of crude oil (petroleum) in US dollars per barrel. Source: IndexMundi
http://www.indexmundi.com/commodities/?commodity=crude-oil&months=240
Pgasoline – the price of gasoline in US dollars per gallon. Source: IndexMundi
http://www.indexmundi.com/commodities/?commodity=gasoline&months=240
p= 𝑃−𝑃−1𝑃−1
– the growth rate of prices (price index): y1usa, y2usa, ychina, luzbekistan, pcotton,
pgold, psilver, pcrudeoil, pgasoline - growth rates for Y1USA, Y2USA, YChina, LUzbekistan, Pcotton, Pgold,
Psilver, Pcrudeoil, and accordingly Pgasoline.
42
Table A1. Test for stationarity (ADF-test)
Indicator Sample size n Period 𝐷𝐹 =�̂�
𝑆𝐸(�̂�)
Ybelarus 69 1994:1-2011:1 -2.356 Ybelarus 68 1994:2-2011:1 -4.715 Ubelarus 66 1994:4-2011:1 -2.236 Δubelarus 65 1995:1-2011:1 -3.613 Yrussia 65 1995:1-2011:1 -2.656 Yrussia 64 1995:2-2011:1 -7.102 Urussia 32 2003:1-2010:4 -3.215 Δurussia 31 2003:2-2010:4 -5.969 Ymoldova 33 2003:1-2011:1 -4.825 Ymoldova 32 2003:2-2011:1 -5.430 Umoldova 29 2004:1-2011:1 -3.160 Δumoldova 28 2004:2-2011:1 -6.317 Yukraina 32 2003:1-2010:4 -3.646 Yukraina 31 2003:2-2010:4 -5.358 Uukraina 24 2005:1-2010:4 -2.743 Δuukraina 23 2005:2-2010:4 -4.465 Yuzbekistan 46 2000:1-2011:2 -4.093 Yuzbekistan 45 2000:2-2011:2 -7.582 Uuzbekistan 28 2000:1-2006:4 -4.604 Δuuzbekistan 27 2000:2-2006:4 -5.776 Luzbekistan 28 2000:1-2006:4 -4.054 Luzbekistan 27 2000:2-2006:4 -5.584 Y1usa 257 1947:1-2011:1 0.621 y1usa 256 1947:2-2011:1 -9.453 Y2usa 257 1947:1-2011:1 -1.514 y2usa 256 1947:2-2011:1 -11.018 Ychina 41 2001:1-2011:1 -2.360 Ychina 40 2001:2-2011:1 -6.939 Pcotton 80 1991:2-2011:1 2.994 Pcotton 79 1991:3-2011:1 -5.897 Pcrudeoil 80 1991:2-2011:1 -2.556 Pcrudeoil 79 1991:3-2011:1 -6.693 Pgasoline 80 1991:2-2011:1 -2.999 Pgasoline 79 1991:3-2011:1 -8.075 Pgold 80 1991:2-2011:1 1.591 Pgold 79 1991:3-2011:1 -8.095 Psilver 80 1991:2-2011:1 2.084 Psilver 79 1991:3-2011:1 -7.908 CPI 77 1992:1-2011:1 -1.840
Note: Checks Dickey-Fuller test based on regression ∆Yt=β0+αt +δYt-1 +εt. Тест H0: δ =0 0 is carried out for statistical 𝐷𝐹 = 𝛿�
𝑆𝐸(𝛿�) on the basis of Table DF.
Table DF. Large-Sample Critical Values of the Augmented Dickey_Fuller Statistic
Deterministic Regressors 10% 5% 1% Intercept only -2.57 -2.86 -3.43 Intercept and time trend -3.12 -3.41 -3.96
Source: Stock, J.H., Watson, M.W. (2007). Introduction to Econometrics. Charter 14, p. 563.
43
Appendix B. Methodology
B.1. The method of instrumental variables (IV)
Suppose that, in regression (1’), the regressor y is random. Further, suppose that the
assumption that the error ε is uncorrelated with the regressor y does not hold, that is
corr (y, ε) ≠ 0.
One can obtain consistent estimates of the coefficients in the regression using a set of
instrumental variables (instruments, IV) Z=(z1,…, zm) that satisfy the following conditions.
• The instruments Z are sufficiently strongly correlated with the regressor y, that is, the
instruments are relevant:
corr(zi, y) ≠ 0, i =1,…, m
(instrument relevance condition).
• The instruments Z are uncorrelated with the error ε, that is, the instruments are exogenous
(otherwise, the IV method gives inconsistent estimates similar to the OLS):
corr(zi, ε) = 0, i =1,…, m
(instrument exogeneity condition);
Instruments Z that satisfy the above relevance and exogeneity conditions are referred to
as valid instruments (and the conditions are referred to as instrument validity conditions).
Having selected the instruments satisfying the above assumptions, one can estimate the
regression parameters using the two stage least squares (TSLS) procedure.
1. The first stage of the procedure regresses y on the instruments Z=(z1,…, zm): y=a+b1 z1 +…+bm zm + ν. (B1)
One then calculates the predicted values 𝑦� of the dependent variable y using estimated
regression (B1).
2. In the second stage, the dependent variable Δu is regressed on the predicted values 𝑦�
from first stage regression (B1):
Δu = α – β𝑦� + error.
In the case where there are exogenous regressors in the model, they are included in the
right-hand side of first stage regression (B1), in addition to the instrumental variables. The TSLS
procedure is also generalized to the case of a number k≥1 of endogenous regressors in a natural
way (see, for instance, Ch. 12 in Stock and Watson, 2007).
The TSLS estimates of the parameters α and β are the estimates from the second stage
regression. The main idea of the TSLS procedure is to use a regressor that is “cleaned from
errors”.
44
The instruments that explain little of the variation in the regressor y and thus do not
satisfy the relevance condition are called weak instruments. One way to check for weak
instruments is to consider the first stage F-statistic, that is, the F-statistic for testing the
hypothesis that the coefficients on the instruments in first stage regression (B1) are all zero: b1
=…=bm=0. Naturally, sufficiently large values of the first stage F-statistic indicate that the
instrument relevance condition is satisfied, that is, the instruments used are not weak. A simple
rule of thumb is that, in the case of a single endogenous regressor, one does not need to worry
about weak instruments if the first stage F-statistic exceeds 10 (see Ch. 12 in Stock and Watson,
2007). We note that most of the models in this paper have a single endogenous regressor given
by the output growth rate or the change in the unemployment rate.
In the case where the number m of instruments is greater than the number k of
endogenous regressors (e.g., when there is a single endogenous regressors, as in most of the
models considered in this paper, and there are two or more instruments available), the condition
on exogeneity of the instruments can be assessed using the following overidentifying restrictions
J-test described in Stock and Watson (2007), Ch. 12, Section 12.3. Let et denote the residuals
from the estimated TSLS regression. Using the OLS, one estimates the coefficients in the
regression of the residuals on the instruments zi, i=1,..., m (and exogenous regressors, if any):
e=δ0+ δ1 z1+ …+ δm zm+u (B2)
Let F denote the homoskedasticity-only F-statistic testing the hypothesis the coefficients at the
instrumental variables in (B2) are all zero: δ1 = ... = δm = 0. The overidentifying restrictions J-
statistic is J = mF. Under the null hypothesis that all the instruments are exogenous, if the error
term u is homoskedastic then the distribution of the J-statistic is approximately χ2m-k in large
samples. The number m-k of degrees of freedom is the “degree over-identification” that equals to
the number of instruments minus the number of endogenous regressors. Thus, a sufficiently large
value of the J-statistic calculated for the data presents evidence against instrument exogeneity.
Vice versa, a sufficiently small value of the J-statistic for the data at hand indicates that the
instrument exogeneity condition is satisfied.
With an appropriate selection of instruments, the IV method yields consistent estimates
of the model parameters in (1’). However, there remains a problem with standard errors of the
regression coefficients. This problem is discussed, among others, in Orlov (2002) and Stock and
Watson (2007, Ch. 12). For example, Stock and Watson (2007) indicate in Ch. 12, p. 437, that
“there are two points to bear in mind about TSLS standard errors. First, the standard errors
reported by OLS estimation of the second-stage regression are incorrect because they do not
recognize that it is the second stage of a two-stage process. Specifically, the second-stage OLS
standard errors fail to adjust for the fact that the second-stage regression uses the predicted
45
values of the included endogenous variables. Formulas for standard errors that make the
necessary adjustment are incorporated into (and automatically used by) TSLS regression
commands in econometric software. Therefore this issue is not a concern in practice if we use a
specialized TSLS regression command. Second, as always the error u might be heteroskedastic.7
It is therefore important to use heteroskedasticity-robust versions of the standard errors, for
precisely the same reason as it is important to use heteroskedasticity-robust standard errors for
the OLS estimators of the multiple regression model.”
While implementing the IV methods in the report, we calculate and report robust standard
errors of the TSLS regression coefficients. The robust standard errors are then used to construct
the corresponding confidence intervals of the coefficients.
B.2. Confidence intervals for elasticity using the delta method
Throughout this section, n denotes the sample size that is assumed to be large.
Consider equation (12) in Section 4.1.4: U= α+ β log (Y). For a given value of Y,
determine the confidence interval for the coefficient of elasticity of U with respect to 𝑌 = 𝑒𝑈−𝛼𝛽 ,
that is, the confidence interval for the value of the function
𝜀𝑌(𝑈) =𝛽𝑈
=𝛽
𝛼 + 𝛽log (𝑌).
Consider the vector �𝛼𝛽� and the function ℎ(𝛼,𝛽) = 𝛽
𝛼+ 𝛽log (𝑌) for a given value of Y. Denote by
𝛾 the gradient of h: 𝛾 = ∇ℎ, that is,
𝛾 = �𝜕ℎ𝜕𝛼𝜕ℎ𝜕𝛽
� = �−𝛽
(𝛼+𝛽log (𝑌))2𝛼
(𝛼+𝛽log (𝑌))2�.
For a given value Y, a natural plug-in estimate of the gradient 𝛾 is given by
γ� =
⎝
⎜⎛
−�̂�(𝛼� + �̂�log (𝑌))2
𝛼�(𝛼� + �̂�log (𝑌))2⎠
⎟⎞
,
where 𝛼� and �̂� are estimates of 𝛼 and 𝛽 (e. g., obtained using the TSLS, as in the case of
Russia above).
The TSLS estimates 𝛼� and �̂� are asymptotically normal:
�𝛼��̂��~𝑁��𝛼𝛽� ,𝛴𝑛�
7 u· is the error term denoted by ε in this section, which may represent measurement error and/or omitted factors.
46
(here 𝑓(𝑛)~𝑁(𝑚,𝐷) means that f(n) can be approximated by a normal distribution with
parameters m and D for large n).
An estimate 𝛴� of the variance-covariance matrix 𝛴 = 𝛴𝑛 of the asymptotic normal
distribution of 𝛼� and �̂� is provided by econometric and statistical software for OLS and TSLS
estimation procedures. Naturally, its diagonal elements are the squares of standard errors of the
coefficients 𝛼 and 𝛽 (see also Draper and Smith, 1981, Ch. 2, Section 2.3, for a related
discussion and further formulas for 𝛴� in the case of the OLS).
According to the delta method, for a given value of y one has 𝛽�
𝛼�+𝛽�log (𝑦)~𝑁 � 𝛽
𝛼+𝛽log (𝑦),σ𝑛2�,
where σ𝑛2 = 𝛾𝑇 ∙ 𝛴𝑛 ∙ 𝛾. A natural plug-in estimate σ�2 for the asymptotic variance σ2 = σ𝑛2 in
the above relation is given by σ�2 = γ�𝑇∙ 𝛴� ∙ γ�.
Consider model (11) whose statistical characteristics are provided in Table 4.4.
The estimate 𝛴� of the variance-covariance matrix 𝛴 (provided by STATA) is
𝛴� = � 0.00168 −0.00019−0.00019 0.000022�
(as discussed above, the diagonal elements of the matrix 𝛴� are the squares of the standard errors
of the regression coefficients estimated in Table 4.3: 0.00168 = 𝑠𝛼�2=(0.04101)2 and 0.000022 =
𝑠𝛽�2=(0.00466)2).
Calculate
σ�2 = γ�𝑇∙ 𝛴� ∙ γ� = � −𝛽�
(𝛼�+𝛽�𝑙𝑛𝑌)2; 𝛼�
(𝛼�+𝛽�𝑙𝑛𝑌)2� � 0.00168 −0.00019−0.00019 0.000022��
−𝛽�
(𝛼�+𝛽�𝑙𝑛𝑌)2
𝛼�(𝛼�+𝛽�𝑙𝑛𝑌)2
�=
= 1(𝛼�+𝛽�𝑙𝑛𝑌)4
�−�̂�;𝛼�� � 0.00168 −0.00019−0.00019 0.000022� �
−�̂�𝛼��=
= 1(0.23693 − 0.01856ln𝑌)4
( 0.01856; 0.23693) � 0.00168 −0.00019−0.00019 0.000022� �
0.018560.23693�=
=1.278E − 07
(0.23693 − 0.01856log (𝑌))4.
Thus, the (1-α)100% confidence interval for the elasticity coefficient
𝜀𝑌(𝑈) =𝛽𝑈
= −0.01856
0.23693 − 0.01856log (𝑌)
is given by
�− 0.018560.23693 − 0.01856ln𝑌
± 𝑧∝2�∙ 1.278E−07
(0.23693 − 0.01856ln𝑌)4�,
47
where 𝑧∝2�
= Ф−1(𝛼 2� ) and Ф(𝑥) = 1√2𝜋
∫ 𝑒𝑢22�
𝑥−∞ 𝑑𝑢 is the standard normal cdf. Figure 4.1
presents the 95% confidence interval for the coefficient 𝜀𝑌(𝑈) of elasticity of the unemployment
rate with respect to the GDP level in Russia.
Consider now the coefficient of elasticity of Y with respect to U. According to the
estimates in Table 4.4, Model 2, one has
log (YRussia)=12.77 - 53.887 Urussia
or, in the general form,
log (Y)=c+kU.
The coefficient of elasticity of Y with respect to U is given by
𝜀𝑈(𝑌) = 𝑑𝑌𝑑𝑈∙ 𝑈𝑌
= 𝑘𝑈.
Let 𝑔(𝑐,𝑘) = 𝑘𝑈 for a given U. Then 𝜕𝑔(𝑐,𝑘)𝜕𝑐
= 0; 𝜕𝑔(𝑐,𝑘)𝜕𝑘
= 𝑈.
Denote by 𝛾 = ∇𝑔 the gradient of g, that is,
𝛾 = �𝜕𝑔𝜕𝑐𝜕𝑔𝜕𝑘
� = �0𝑈�.
Then, by the delta method, for a given value of U one has
𝑘�𝑈~𝑁(𝑘𝑈,σ𝑛2),
where the asymptotic variance σ𝑛2 = σ2 is given by σ2 = 𝛾𝑇 ∙ 𝛴𝑛 ∙ 𝛾, and 𝛴𝑛 is the variance-
covariance matrix of the asymptotic normal distribution for estimates �̂� and 𝑘� of the parameters
c and 𝑘 (e. g., those obtained by the TSLS):
��̂�𝑘��~𝑁 ��𝑐𝑘� ,𝛴𝑛�.
It is easy to see that σ2 = 𝛾𝑇 ∙ 𝛴𝑛 ∙ 𝛾 = 𝑈2𝜎𝑘2, where 𝜎𝑘2 is the asymptotic variance of
the estimate 𝑘�. Thus, for a given value of U, the estimate for σ2 is given by σ�2 = 𝑈2𝑠𝑘2, where
𝑠𝑘 is the standard error on the coefficient k.
For Model 2 of Table 4.4 we have 𝑠𝑘2=13.532=183.17. Consequently, the (1-α)100%
confidence interval for the elasticity coefficient
𝜀𝑈(𝑌) = 𝑘𝑈 =-53.887U
is given by �−53.887𝑈 ± 𝑧∝2�∙ 183.17𝑈2�.
Figure 4.2 presents the confidence intervals for the coefficient of elasticity of the Russian
GDP level with respect to the unemployment rate.
48
Appendix C. Confidence and prediction intervals for a regression
If the standard assumptions that the regression errors are normal with mean zero and a
constant variance, one can use the following procedure for calculating the regression confidence
and prediction intervals that is described in Yakovleva (2008) and Draper and Smith (1986).
Consider the linear regression 𝑦𝑖 = 𝛽0 + 𝛽1𝑥𝑖 + 𝜀𝑖, where yi are the values of the dependent
variable, i=1,…,n; xi are the values of the independent variable; β0, β1 are the regression
coefficients to be estimated; and εi denote the (random) regression error. Let the regression errors
be random variables that follow a normal distribution with mean zero and the variance 𝐺2:
𝜀𝑖~𝑁(0,𝐺2).
Using the regression model 𝑦𝑖 = 𝛽0 + 𝛽1𝑥𝑖 + 𝜀𝑖, calculate the predicted value ym for a
given value xm. For the bivariate linear regression model, a point prediction of y for a given value
xm of the independent variable has the following form:
𝑦𝑚 = 𝛽0 + 𝛽1𝑥𝑚.
For the significance level α, the point estimate of the predicted value ym belongs to the
interval that is calculated using the formula
𝑦𝑚 − 𝑡(𝑛−2; 𝛼2)𝜔(𝑚) ≤ 𝑦𝑚 ≤ 𝑦𝑚 + 𝑡(𝑛−2; 𝛼2)𝜔(𝑚).
Here 𝑡(𝑛−2; 𝛼2) denotes the critical value of Student’s t-distribution with с n−2 degrees of freedom
(in the case of a bivariate regression model) for the given significance level α; and ω(m) denotes
the prediction error at point m.
The prediction error ω(m) is calculated using the formula
𝜔(𝑚) = �𝑆2(𝜀) ∙ �𝑛 + 1𝑛
+(𝑥𝑚 − �̅�)2
∑ (𝑥𝑖 − �̅�)2𝑛𝑖=1
�
where S2(ε) is unbiased estimate of the variance of the error in the bivariate regression.
Let us describe how the above formulas are derived. Consider the bivariate regression
model
𝑦𝑖 = 𝛽0+𝛽1(𝑥𝑖 − �̅�) + 𝜀𝑖,
where the independent variable x is represented in the centered form. One needs to construct the
prediction of the dependent variable y for a given value of the independent variable xm:
𝑦𝑚 = 𝛽�0+𝛽�1(𝑥𝑚 − �̅�) + 𝜀𝑚,
where 𝛽�0, 𝛽�1 are estimates of the regression parameters 𝛽0, 𝛽1.
The expectation of the dependent variable y at point m is determined as
𝐸(𝑦𝑚/𝑥𝑚) = 𝛽�0+𝛽�1(𝑥𝑚 − �̅�) + 𝜀𝑚.
The variance of the dependent variable y at point m is given by
49
𝐷 �𝑦𝑚 𝑥𝑚
− �̅�� = 𝐷(𝛽�0+𝛽�1(𝑥𝑚 − �̅�) + 𝜀𝑚) = 𝐷(𝛽�0)+𝐷(𝛽�1(𝑥𝑚 − �̅�)) + 𝐷(𝜀𝑚) =
= 𝐺2
𝑛+(𝑥𝑚 − �̅�)2 ∙ 𝐺2
∑ (𝑥𝑖−�̅�)2𝑛𝑖=1
+ 𝐺2,
where D(β0) is the variance of the estimate of the parameter β0 of the bivariate regression. The
variance D(β0) is calculated using the formula
𝐷�𝛽�0� = 𝐷�𝛽0 +∑𝜀𝑖𝑛� = 𝐷�
∑𝜀𝑖𝑛� =
1𝑛2�𝐷(𝜀𝑖) =
𝑛𝐺2
𝑛2=𝐺2
𝑛.
A point estimate of the prediction of the variable ym has a normal distribution with mean
𝛽�0+𝛽�1(𝑥𝑚 − �̅�) and the variance
𝐺2 ∙ �𝑛+1𝑛
+ (𝑥𝑚−�̅�)2
∑ (𝑥𝑖−�̅�)2𝑛𝑖=1
�.
Therefore,
𝑦𝑚/𝑥𝑚~𝑁�𝛽�0 + 𝛽�1(𝑥𝑚 − �̅�); 𝐺2 ∙ �𝑛+1𝑛
+ (𝑥𝑚−�̅�)2
∑ (𝑥𝑖−�̅�)2𝑛𝑖=1
��.
If the sample estimate S2 of G2 is used instead of the variance G2 in the expression for the
variance of the dependent variable y at point m, then one obtains the following confidence
interval for the prediction of the dependent variable for the given value xm of the independent
variable:
𝑦𝑚 𝑥𝑚 ∈⁄ �𝛽�0 + 𝛽�1(𝑥𝑚 − �̅�) ± 𝑡(𝑛−2; 𝛼2) ��𝑆2 �𝑛 + 1𝑛
+(𝑥𝑚 − �̅�)2
∑ (𝑥𝑖 − �̅�)2𝑛𝑖=1
���.
The estimate S2 for the model of the bivariate linear regression is calculated using the following
formula:
𝑆2 = ∑ 𝑒𝑖2𝑛
𝑖=1𝑛−2
.
The prediction interval can be written as
𝑦𝑚 𝑥𝑚⁄ ∈ �𝛽�0 + 𝛽�1(𝑥𝑚 − �̅�) ± 𝑡(𝑛−2; 𝛼2) ��∑ 𝑒𝑖2𝑛𝑖=1𝑛 − 2
�𝑛 + 1𝑛
+(𝑥𝑚 − �̅�)2
∑ (𝑥𝑖 − �̅�)2𝑛𝑖=1
���.
Draper and Smith (1986) note that, in order to obtain the join confidence curves that hold for the
whole regression in its entirety, one should change 𝑡(𝑛−2; 𝛼2) to �2𝐹(2,𝑛 − 2,𝛼), where F(2,n-
2,α) is the quantile of an F-distribution with (2; n-2) degrees of freedom for the significance level
α (see also Zacks, 1971). Then
𝑦𝑚 𝑥𝑚⁄ ∈ �𝛽�0 + 𝛽�1(𝑥𝑚 − �̅�) ± �2𝐹(2,𝑛 − 2,𝛼) ��∑ 𝑒𝑖2𝑛
𝑖=1𝑛−2
�𝑛+1𝑛
+ (𝑥𝑚−�̅�)2
∑ (𝑥𝑖−�̅�)2𝑛𝑖=1
���. (C1)
50
If we restrict ourselves to the confidence intervals for the average value 𝑦�𝑚 of the dependent
variable y at point m, then the estimate of the standard deviation of 𝑦�𝑚 has the form
�𝑆2 �1𝑛
+ (𝑥𝑚−�̅�)2
∑ (𝑥𝑖−�̅�)2𝑛𝑖=1
�=�∑ 𝑒𝑖2𝑛
𝑖=1𝑛−2
�1𝑛
+ (𝑥𝑚−�̅�)2
∑ (𝑥𝑖−�̅�)2𝑛𝑖=1
�.
Therefore, the confidence interval for 𝑦�𝑚 is given by
𝑦�𝑚 𝑥𝑚⁄ ∈ �𝑦�𝑚 ± �2𝐹(2,𝑛 − 2,𝛼) ��∑ 𝑒𝑖2𝑛
𝑖=1𝑛−2
�1𝑛
+ (𝑥𝑚−�̅�)2
∑ (𝑥𝑖−�̅�)2𝑛𝑖=1
���. (C2)
Thus, for a given significance level 𝛼, relation (C2) determines the confidence interval
for the average value of the dependent variable 𝑦�𝑚 for a given value of the regressor xm. Relation
(C1) provides the interval that contains the values of the dependent variable 𝑦𝑚 for a given value
of the regressor xm and is used for predicting the variable y under a known (or assumed) value of
the regressor x.
51
Appendix D. Confidence and prediction intervals for the regression of changes in the unemployment rate on GDP growth in CIS countries: Estimates for Belarus, Kazakhstan,
Moldova, Russia, Ukraine and Uzbekistan
Similar to Section 4.1.3, in this section we construct confidence and prediction intervals
for the regressions of the change in the unemployment rate on the GDP growth rate for Belarus,
Kazakhstan, Moldova, Russia, Ukraine and Uzbekistan.
Belarus
The following figures are for the regression (see Table E10)
Δubelarus=-0.0004–0.00567ybelarus.
Figure D1. 95% confidence intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Belarus
Figure D2. 95% prediction intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Belarus
-0,006
-0,004
-0,002
-3,5E-17
0,002
-0,2 0 0,2 0,4 0,6 0,8
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Confidence Interval, Belarus
-0,004-0,003-0,002-0,0015E-180,0010,0020,003
-0,2 -0,1 0 0,1 0,2Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Prediction Interval, Belarus
52
Kazakhstan
Figures D3 and D4 are for the regression
Δukazakhstan=-0.00084–0.0073ykazakhstan (see Model 1 of Table E12).
Figure D3. 95% confidence intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Kazakhstan
Figure D4. 95% prediction intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Kazakhstan
-0,006
-0,004
-0,002
4E-18
0,002
0,004
-0,4 -0,2 0 0,2 0,4
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Confidence Interval, Kazakhstan
-0,01
-0,005
2E-17
0,005
0,01
-0,2 -0,1 0 0,1 0,2Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Prediction Interval, Kazakhstan
53
Moldova
Figures D5 and D6 present the confidence and prediction intervals for the regression
Δumoldova=0.0029–0.05936ymoldova
(see Model 2 in Table E11).
Figure D5. 95% confidence intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Moldova
Figure D6. 95% prediction intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Moldova
-0,006
-0,002
0,002
0,006
0,01
-0,045 -0,025 -0,005 0,015 0,035
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Confidence Interval, Moldova
-0,04
-0,02
0
0,02
0,04
-0,2 -0,1 0 0,1 0,2
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Prediction Interval, Moldova
54
Russia
The following Figures D7 and D8 present the confidence and prediction intervals for
Okun’s model for Russia
Δurussia=0.00336-0.0747 yrussia.
(see Model 2 in Table 4.2 of Section 4.1.2).
Figure D7. 95% confidence intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Russia
Figure D8. 95% prediction intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Russia
-0,02
-0,01
1E-17
0,01
0,02
0,03
-0,25 -0,2 -0,15 -0,1 -0,05 5E-16 0,05 0,1 0,15 0,2
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Confidence Interval, Russia
-0,03
-0,01
0,01
0,03
-0,2 -0,1 0 0,1 0,2
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Prediction Interval, Russia
55
Uzbekistan
The following diagrams are for the Okun’s law regression for Uzbekistan
Δuuzbekistan=0.0058 – 0.0663yuzbekistan
(see Model 1 in Table E7):
Figure D9. 95% confidence intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Uzbekistan
Figure D10. 95% prediction intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Uzbekistan
-0,04
-0,02
0
0,02
0,04
-0,4 -0,2 0 0,2 0,4 0,6
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Confidence Interval, Uzbekistan
-0,03-0,02-0,01
00,010,020,030,04
-0,2 -0,1 0 0,1 0,2
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Prediction Interval, Uzbekistan
56
Ukraine
Figures D11 and D12 provide the confidence and prediction intervals for Okun’s law in
Ukraine (Model 6 in Table E8):
Δuukraine=0.00316– 0.0512yukraine. Figure D11. 95% confidence intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Ukraine
Figure D12. 95% prediction intervals for the regression of the change in the unemployment rate
on the GDP growth rate in Ukraine
-0,004
-0,002
-1E-18
0,002
0,004
0,006
-0,015 -0,005 0,005 0,015 0,025 0,035
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Confidence Interval, Ukraine
-0,02
-0,01
0
0,01
0,02
0,03
-0,2 -0,1 0 0,1 0,2
Cha
nge
of th
e U
nem
ploy
men
t
GDP Growth
95% Prediction Interval, Ukraine
57
Appendix E. Tables and figures
Table E1. Regression of changes in GDP growth and unemployment in Russia on the variables q1, q2, q3
Dependent variable yrussia Δurussia
Independent variable Coefficient
Robust std.
error
[95% confid. interval] Coefficient
Robust std.
error
[95% confid. interval]
cons q1 q2 q3
0.0430 -0.1469** 0.0788** 0.0976**
0.0210 0.0297 0.0226 0.0219
[-0.000; 0.086] [-0.208; -0.086] [0.033; 0.125] [0.053; 0.142]
0.0038 0.0064*
-0.0160** -0.0075**
0.0016 0.0034 0.0023 0.0022
[0.0007; 0.007] [-0.0005; 0.013] [-0.021; -0.011] [-0.012; -0.003]
R2
F(R2) 0.847 46.05
0.724 23.64
Sample size n = 31 (2003:2-2010:4) Note: The regression coefficients are significant at the significance level of *5% or **1%.
Table E2. TSLS regression of changes in the unemployment rate on the GDP growth rate in
Russia
Dependent variable: change in unemployment Δurussia Regressors (1) (2) (3) (4) (5) (6)
yrussia -0.0664** (0.0094)
-0.0592** (0.0206)
-0.0747** (0.0109)
-0.0691** (0.0105)
-0.0627** (0.0130)
-0.0567** (0.0109)
pgold --- --- --- 0.0358048
* (0.0170)
--- ---
q1 --- -0.0023 (0.0038) --- --- --- ---
q2 -0.0094** (0.0018)
-0.0113** (0.0028) --- --- -0.0097**
(0.0022) -0.0102** (0.0019)
q3 --- -
0.0017671 (0.0033)
--- --- --- ---
const 0.0053** (0.0012)
0.0064** (0.0015)
0.0034* (0.0013)
0.0014 (0.0018)
0.0052** (0.0011)
0.0050** (0.0012)
R2 0.768 0.783 0.596 0.653 0.773 0.776
F(m,n-m-1) F(2, 28) = 48.4
F( 4, 26) = 24.55
F( 1, 29) = 47.22
F( 2, 28) = 34.45
F( 2, 28) = 47.81
F( 2, 28) = 41.33
Prob>F 0.0000 0.0002 0.0000 0.0000 0.0000 0.0000
Instrumental variables
ychina, pcudeoil,
pgold pcrudeoil pcrudeoil,
q1, q2, q3 pcrudeoil, q1, q2, q3 pcrudeoil pcrudeoil,
q1, q3
First stage F-statistic
F(3,27)= 11.56
F( 1, 59) = 11.58
F( 4, 59) = 38.18
F( 4, 58) = 39.05
F( 1, 61) = 7.44
F( 3, 59) = 47.87
J-test and p-value
0.00 1.00
0.00 1.00
0.00 1.00
0.00 1.00
0.00 1.00
0.00 1.00
Note: The regression is estimated using quarterly data on the variables. Standard errors are given in parentheses under the coefficients. Individual coefficients are statistically significant at the *5% or **1% level.
58
Table E3. TSLS regression of changes in the unemployment rate on the GDP growth rate in
Russia
Δurussia [95% Conf. Interval] Δurussia [95% Conf.
Interval] Regressors (3) (6)
yrussia -0.0747** (0.0109)
[-0.097; -0.052]
-0.0567** (0.0109)
[-0.079; -0.034]
q2 --- --- -0.0102** (0.0019)
[-0.014; -0.006]
const 0.0034* (0.0012582)
[0.001; 0.006]
0.0050** (0.0012)
[0.003; 0.007]
R2 0.596 0.776 F(m,n-m-1) F(1, 29) = 47.22 F(2, 28) = 41.33 Prob>F 0.0000 0.0000 Instrumental variables pcrudeoil, q1, q2, q3 pcrudeoil, q1, q3 First stage F-statistic F(4, 59) = 38.18 F(3, 59) = 47.87 J-test and p-value
0.00 1.00
0.00 1.00
59
Table E4. TSLS rolling regression of changes in the unemployment rate on the GDP growth rate in Russia
Regressors Δurussia [95% Conf.Interval] Δurussia [95% Conf.Interval] Δurussia [95% Conf.Interval] Δurussia [95% Conf.Interval] (1) (2) (3) (4)
yrussia -0.0475** (0.0138)
[-0.077; -0.018]
-0.0485** (0.0139)
[-0.078, -0.019]
-0.0447 ** (0.0149)
[-0.076, -0.013]
-0.0455** (0.0133)
[-0.074, -0.017]
q2 -0.0102** (0.0025)
[-0.016; -0.005]
-0.0105** (0.0027)
[-0.016, -0.005]
-0.0113 ** (0.0029)
[-0.017, -0.005]
-0.0116** (0.0029)
[-0.018, -0.005]
const 0. 0044* (0. 0017)
[0.001; 0.008]
0.0044* (0.0017)
[0.001, 0.008]
0.0047 * (0.0017)
[0.001, 0.008]
0.0051** (0.0016)
[0.002, 0.008]
R2 0.695 0.715 0.702 0.729 F(m,n-m-1)=F(2,17) 16.01 17.76 17.92 20.79 Prob>F 0.0001 0.0001 0.0001 0.0000 Sample 2003:2-2008:1 2003:3-2008:2 2003:4-2008:3 2004:1-2008:4 (5) (6) (7) (8)
yrussia -0.0512** (0.0133)
[-0.079, -0.023]
-0.0513** (0.0135)
[-0.080, -0.023]
-0.0558** (0.0143)
[-0.086, -0.026]
-0.0582** (0.0139)
[-0.088, -0.029]
q2 -0.0112** (0.0029)
[-0.017, -0.005]
-0.0093** (0.0022)
[-0.014, -0.005]
-0.0084** (0.0024)
[-0.014, -0.003]
-0.0075** (0.0022)
[-0.012, -0.003]
const 0.0055** (0.0016)
[0.002, 0.009]
0.0055** (0.0016)
[0.002, 0.009]
0.0052** (0.0016)
[0.002, 0.009
0.0046** (0.0015)
[0.002, 0.008]
R2 0.765 0.759 0.748 0.787 F(m,n-m-1)=F(2,17) 22.16 25.15 25.60 26.39 Prob>F 0.0000 0.0000 0.0000 0.0000 Sample 2004:2-2009:1 2004:3-2009:2 2004:4-2009:3 2005:1-2009:4 (9) (10) (11) (12)
yrussia -0.0624** (0.0113)
[-0.086, -0.034]
-0.0613 (0.0114)
[-0.085, -0.037]
-0.0663** (0.0114)
[-0.090, -0.042]
-0.0656** (0.0113)
[-0.089, -0.042]
q2 -0.0075** (0.0022)
[-0.012, -0.003]
-0.0090 (0.0023)
[-0.014, -0.004]
-0.0079** (0.0024)
[-0.013, -0.003]
-0.0081** (0.0023)
[-0.013, -0.003]
const 0.0052** (0.0011)
[0.003, 0.008]
0.0052 (0.0011)
[0.003, 0.008]
0.0047** (0.0011)
[0.0024, 0.007]
0.0048** (0.0011)
[0.002, 0.007]
R2 0.855 0.857 0.860 0.857 F(m,n-m-1)=F(2,17) 43.01 42.73 45.77 45.05 Prob>F 0.0000 0.0000 0.0000 0.0000 Sample 2005:2-2010:1 2005:3-2010:2 2005:4-2010:3 2006:1-2010:4
Note: The regressions are estimated using pcrudeoil, q1 and q3 as instrumental variables. Robust standard errors are given in parentheses under the coefficients.
60
Table E5. The coefficients of the rolling regression Δurussia=α·yrussia+β·q2+const and the boundaries of the 95% confidence intervals [Δ1, Δ2] for the coefficient α. Period 2003:2-2008:1 2003:3-2008:2 2003:4-2008:3 2004:1-2008:4
α -0.0475 -0.0485 -0.0447 -0.0455 Δ1 -0.0767 -0.0779 -0.0760 -0.0740 Δ2 -0.0180 -0.0191 -0.0130 -0.0170 β -0.1016 -0.0105 -0.0113 -0.0116
const 0.0044 0.0044 0.0047 0.0051
Period 2004:2-2009:1 2004:3-2009:2 2004:4-2009:3 2005:1-2009:4 α -0.0512 -0.0513 -0.0558 -0.0582 Δ1 -0.0793 -0.0797 -0.0858 -0.0880 Δ2 -0.0231 -0.0229 -0.0257 -0.0290 β -0.0112 -0.0093 -0.0084 -0.0135
const 0.0055 0.0055 0.0052 0.0018 Period 2005:2-2010:1 2005:3-2010:2 2005:4-2010:3 2006:1-2010:4
α -0.0624 -0.0613 -0.0663 -0.0656 Δ1 -0.0863 -0.0853 -0.0904 -0.0890 Δ2 -0.0385 -0.0372 -0.0422 -0.0420 β -0.0075 -0.0090 -0.0079 -0.0081
const 0.0052 0.0052 0.0047 0.0048
61
Table E6. Regression of rate of GDP growth and changes in the unemployment rate in Uzbekistan on the variables q1, q2, q3
Dependent variable yuzbekistan Δuuzbekistan Independent variable Coefficient Robust std. error [95% confidence interval] Coefficient Robust std. error [95% confidence interval]
cons q1 q2 q3
0.1515** -0.5254** 0.1994** 0.2571***
0.0225 0.0241 0.0293 0.0443
[0.106; 0.197] [-0.574; -0.477] [0.140; 0.258] [0.168; 0.347]
-0.0040* 0.0355** -0.0180** -0.0138**
0.0017 0.0030 0.0018 0.0031
[-0.007; -0.0005] [0.029; 0.042]
[-0.022; -0.014] [-0.020; -0.007]
R2
F(R2) 0.94
591.82 0.948 154.18
Sample size n = 45 (2000:2-2011:2) n = 27 (2000:2-2006:4)
Table E7. TSLS regression of changes in the unemployment rate on GDP growth rate in Uzbekistan Dependent variable: change in unemployment Δuuzbekistan
Regressors (1) [95% confid. interval] (2) [95% confid.
interval] (3) [95% confid. interval]
yuzbekistan -0.0663**(0.0052) [-0.077; -0.056] -0.0666**(0.0046) [-0.076; -0.057] -0.0661** (0.0043) [-0.075; -0.057] Δuuzbekistan(-1) --- --- -0.2002**(0.0491) [-0.302; -0.098] r --- -0.0043 (0.0031) [-0.011; 0.002] -0.0045 (0.0026) [-0.010; 0.001] const 0.0058**(0.0015) [0.003; 0.009] 0.0078**(0.0019) [0.004; 0.012] 0.0073**(0.0019) [0.003; 0.011] R2 0.866 0.876 0.918 F(m,n-m-1) F(1, 25) = 161.56 F( 2, 24) = 103.59 F(3, 22) = 109.67 Prob>F 0.0000 0.0000 0.0000 Instrumental variables luzbekistan, q1, q3
First stage F-statistic F(3, 23) = 161.87 F(3, 22) = 252.09 F( 3, 20) = 520.02
J-test and p-value
F(3, 23) = 0.00 1.00
F(3, 22) =0.00 1.00
F(3, 20) =0.00 1.00
Note: The regressions are estimated using n = 27 quarterly observations on the variables for the period 2000:2-2006:4. Robust standard errors are given in parentheses under the coefficients. Individual coefficients are statistically significant at *5% or **1% level.
62
Table E8. TSLS regression of changes in the unemployment rate on the GDP growth rate in
Ukraine
Dependent variable: change in unemployment Δuukraine Regressors (1) (2) (3) (4) (5) (6)
yukraine -0.0934 (0.0688)
-0.0496** (0.0167)
-0.0527** (0.0141)
-0.0523** (0.0143)
-0.0514** (0.0129)
-0.0512** (0.0127)
q2 0.0138 (0.0216)
-0.0021 (0.0018) - - - -
q3 0.0171 (0.0220) - - - - -
q4 0.0086 (0.0121) - - - - -
const -0.0043 (0.0094)
0.0036 (0.0017)
0.0033 (0.0019)
0.0032 (0.0019)
0.0032 (0.0018)
0.0032 (0.0018)
R2 0.685 0.710 0.696 0.697 0.698 0.698
F(m,n-m-1) F(4,18)= 9.77
F(2,20) = 20.56
F(1, 21) = 14.02
F( 1, 21) = 13.36
F(1, 21) = 15.94
F(1, 21) = 16.22
Prob>F 0.0002 0.0000 0.0012 0.0015 0.0007 0.0006
Instrumental variables
yrussia, pcotton
yrussia, pcotton
yrussia, pcotton, q2
yrussia, pcotton
yrussia, pcotton, q2,
q3, q4
yrussia, q2, q3, q4
First stage F-statistic
F(2, 25) = 9.07
F(2, 27) = 115.60
F(3, 27) = 105.19
F(2, 28) = 151.47
F(5, 25) = 144.34
F(4, 26) = 187.18
J-test and p-value
0.00 1.00
0.00 1.00
0.00 1.00
0.00 1.00
0.00 1.00
0.00 1.00
Note: The regressions are estimated using n = 27 quarterly observations on the variables for the period 2000:2-2010:4. Robust standard errors are given in parentheses under the coefficients. Individual coefficients are statistically significant at *5% or **1% level.
Table E9. TSLS regression of changes in the unemployment rate on the GDP growth rate in
Ukraine
Dependent variable: change in unemployment Δuukraine Regressors (2) [95% Conf. Interval] (6) [95% Conf. Interval]
yukraine -0.0496** (0.0167)
[-0.084; -0.015]
-0.0512** (0.0127)
[-0.078; -0.025]
q2 -0.0021 (0.0018)
[-0.006; 0.002] --
const 0.0036 (0.0017)
[-0.000; 0.007]
0.0032 (0.0018)
[-0.001; 0.007]
R2 0.710 0.698 F(m,n-m-1) F(2,20) = 20.56 F( 1, 21) = 16.22 Prob>F 0.0000 0.0006 Instrumental variables yrussia, pcotton yrussia, q2, q3, q4 First stage F-statistic F( 2, 27) = 115.60 F( 4, 26) = 187.18 J-test and p-value
0.00 1.00
0.00 1.00
63
Table E10. TSLS regression of changes in the unemployment rate on the GDP growth rate in
Belarus
Regressors Dependent variable: change in unemployment Δubelarus [95%Conf.Interval]
ybelarus -0.0057**(0.0016) [-0.009; -0.002] const -0.0004*(0.0002) R2 0.0257 F(m,n-m-1) F(1, 29) = 12.71 Prob>F 0.0013 Instrumental variables yrussia, pgold, pcotton First stage F-statistic F(3, 27)=33.30 J-test and p-value
0.00 1.00
Note: The regressions are estimated using n = 31 quarterly observations on the variables for the period 2003:2-2010:4. Robust standard errors are given in parentheses under the coefficients. Individual coefficients are statistically significant at *5% or **1% level.
Table E11. TSLS regression of changes in unemployment on the rate of GDP growth in Moldova Dependent variable: change in unemployment Δumoldova Regressors (1) [95% Conf. Interval] (2) [95% Conf. Interval]
ymoldova -0.0416** (0.0126)
[-0.067; -0.016]
-0.0594** (0.0139)
[-0.088; -0.031]
q1 0.0136* (0.0052)
[0.003; 0.024] ---
const -0.0016 (0.0025)
[-0.007; 0.004]
0.0029 (0.0026)
[-0.002; 0.008]
R2 0.848 0.406 F(m,n-m-1) F(2, 25) = 11.9 F(1, 26) = 18.2497 Prob>F 0.0002 0.0002 Instrumental variables q2, q3, y2usa q2, q3, y2usa First stage F-statistic F( 3, 27) = 42.25 F( 3, 28) = 62.95 J-test and p-value
0.00 1.00
0.00 1.00
Dependent variable: change in unemployment Δumoldova Regressors (3) [95% Conf. Interval] (4) [95% Conf. Interval]
ymoldova -0.0596** (0.0127)
[-0.086; -0.033]
-0.0461** (0.0110)
[-0.069; -0.023]
Δumoldova(-1) -0.3506** (0.0898)
[-0.536; -0.165]
-0.3935** (0.0917)
[-0.583; -0.204]
q1 --- 0.014909* (0.0055)
[0.004; 0.026]
const 0.0034 (0.0025)
[-0.002; 0.009]
-0.0013 (0.0023)
[-0.006; 0.003]
R2 0.500 0.664 F(m,n-m-1) F(2, 24) = 13.54 F(3, 23) = 14.43 Prob>F 0.0001 0.0000 Instrumental variables q2, q3, y2usa, ymoldova(-1) q2, q3, y2usa, ymoldova(-1) Fist stage F-statistic F( 4, 21) = 88.16 F( 4, 20) = 67.18 J-test and p-value
0.00 1.00
0.00 1.00
Note: The regressions are estimated using n = 28 quarterly observations on the variables for the period 2004:2-2011:1. Robust standard errors are given in parentheses under the coefficients. Individual coefficients are statistically significant at *5% or **1% level.
64
Table E12. TSLS regression for the change in the unemployment rate and the GDP growth rate in
Kazakhstan
Regressors Δukazakhstan [95% Conf. Interval]
Regressors Δukazakhstan [95% Conf. Interval]
(1) (2)
ykazakhstan -0.0073** (0.0017)
[-0.011;-0.004] ykazakhstan -0.0045*
(0.0022) [-0.009; 0.000]
const -0.0008 (0.0005)
[-0.002; 0.000]
q2 -0.0037** (0.0012)
[-0.006; -0.001]
const -0.00004 (0.0005)
[-0.001; 0.001]
R2 0.195 R2 0.424 F(m,n-m-1) F(1, 32) = 18.07 F(m,n-m-1) F(2, 31) = 14.74 Prob>F 0.0000 Prob>F 0.0000 Instrumental variables pcrudeoil, q1, q3 Instrumental
variables pcrudeoil, q1, q3
Fist stage F-statistic F(3, 30) = 107.49 Fist stage F-
statistic F(3, 29) = 95.76
J-test and p-value
0.00 1.00
J-test and p-value
0.00 1.00
Note: 1) Standard errors are given in parentheses under the coefficients; 2) Individual coefficients are statistically significant at *5% or **1% level.
Table E13. The coefficients of the rolling regression Δkazakhstan=α·ykazakstan+β·q2+const and
the boundaries of the 95% confidence intervals [Δ1, Δ2] for the coefficient α.
Period 2003:2-2008:1 2003:3-2008:2 2003:4-2008:3 2004:1-2008:4 α -0.0076 -0.0079 -0.0066 -0.0070 Δ1 -0.0145 -0.0147 -0.0131 -0.0127 Δ2 -0.0006 -0.0011 -0.0002 -0.0012 β 0.0054 -0.0036 -0.0039 -0.0037
const 0.0003 0.0003 0.0004 0.0002 Period 2004:2-2009:1 2004:3-2009:2 2004:4-2009:3 2005:1-2009:4
α -0.0071 -0.0069 -0.0075 -0.0066 Δ1 -0.0123 -0.0122 -0.0129 -0.0114 Δ2 -0.0018 -0.0017 -0.0020 -0.0018 β -0.0037 -0.0027 -0.0025 -0.0025
const 0.0002 0.0002 0.0001 -0.0001 Period 2005:2-2010:1 2005:3-2010:2 2005:4-2010:3 2006:1-2010:4
α -0.0051 -0.0053 -0.0054 -0.0045 Δ1 -0.0104 -0.0105 -0.0109 -0.0093 Δ2 0.0001 0.0000 0.0000 0.0002 β -0.0025 -0.0020 -0.0019 -0.0020
const -0.0003 -0.0003 -0.0003 -0.0005 Period 2006:2-2011:1 2006:3-2011:2 2006:4-2011:3 α -0.0040 -0.0041 -0.0038 Δ1 -0.0086 -0.0087 -0.0085 Δ2 0.0007 0.0005 0.0008 β -0.0020 -0.0013 -0.0014 const -0.0006 -0.0006 -0.0005 Note: The regressions are estimated using the variables pcrudeoil, q1 and q3 as instruments for the regressor
ykazakhstan.
65
Figure E1. GDP growth and changes in the unemployment rate in Russia, 2003:2-2010:4
Figure E2. The change in the unemployment rate and the GDP growth rate in Russia
-0,025
-0,015
-0,005
0,005
0,015
0,025
-0,25
-0,15
-0,05
0,05
0,15
q2 2003
q2 2004
q2 2005
q2 2006
q2 2007
q2 2008
q2 2009
q2 2010
yrussia Δurussia
-0,25
-0,15
-0,05
0,05
0,15
-0,03 -0,015 -5E-17 0,015 0,03
GDP
Grow
th
Change of the Unemployment
Russia
66
Figure E3. The dynamics of the coefficient α in rolling regressions Δurussia=α·yrussia+β·q2+const
(the dotted lines indicate the boundaries ∆𝑡1 and ∆𝑡2 of the 95% confidence intervals for α)
Notes: Dates along the horizontal axis denote the last quarter in the sample period for each rolling regression. Each sample period is 5 years (20 quarters) long.
Figure E4. Dynamics of the official exchange rate of the US dollar to Uzbek Soum in 1995-2009
-0,1000-0,0900-0,0800-0,0700-0,0600-0,0500-0,0400-0,0300-0,0200-0,01000,0000
0,9
1,2
1,5
67
FigureE5. Quarterly dynamics of the unemployment rate in Uzbekistan in 2000-2006
Figure E6. GDP growth rate and changes in the unemployment rate in Uzbekistan, 2000:2-2006:4
Figure E7. The dynamics of the coefficient α in the rolling regression Δukazakhstan=α·ykazakhstan+β·q2+const (the dotted lines indicate the boundaries ∆𝑡1 and ∆𝑡2 of the
95% confidence intervals for α)
0,00
0,04
0,08
0,12
q1 2000
q3 2000
q1 2001
q3 2001
q1 2002
q3 2002
q1 2003
q3 2003
q1 2004
q3 2004
q1 2005
q3 2005
q1 2006
q3 2006
-0,03
-0,01
0,01
0,03
0,05
-0,6
-0,3
0
0,3
0,6
q1 2000
q3 2000
q1 2001
q3 2001
q1 2002
q3 2002
q1 2003
q3 2003
q1 2004
q3 2004
q1 2005
q3 2005
q1 2006
q3 2006
y Δu
-0,0160-0,0140-0,0120-0,0100-0,0080-0,0060-0,0040-0,00200,00000,0020