Download Is the relationship between inflation and capital

Is the relationship between inflation and capital accumulation linear?
Muhammad Khan and Arslan Tariq Rana
Laboratoire d’Economie d’Orléans (LEO), Université d’Orléans, Rue de Blois BP : 6739. 45067 – Orléans - Cedex
2- France.
Abstract: This paper analyzes the effects of inflation on human and physical capital for 104
countries. Our empirical results, based on an instrumental variable 2-SLS model, substantiate the
view that inflation enhances the accumulation of human capital and reduces the accumulation of
physical capital; supporting a substitution effect- between work and education- for the human
capital and a reversed Tobin effect for the physical capital accumulation. Both these effects are,
however, non-linear and are relevant only when inflation crosses certain thresholds. Finally,
different macroeconomic features e.g., financial development and democracy can alter the
sensitivity of relationship between inflation and the factors’ accumulation.
JEL Classifications: E31, E22, J24
Keywords: Inflation, Growth, Human capital, Physical Capital.
1
1.
Introduction
The empirical literature over the last two decades has overwhelmingly supported a
negative and non-linear relationship between inflation and economic growth. Briefly,
inflation effects on growth are considered to be positive at mild inflation rates, strongly
negative after certain thresholds and weakly negative in hyper inflation episodes (see Omay
and Kan, 2010 and López-Villavicencio and Mignon, 2011).1 This dynamic behavior of
output growth at alternative inflation rates can be explained by various factors e.g.,
credibility of central banks at different inflation rates, signaling channel that explains
producers’ response to variable prices, price indexation in high inflation environment, etc.
Besides, one principal factor that has been identified in the literature is the realignment of
factors of production in response to inflation changes (Gillman and Nakov, 2003). To this
view, agents’ decisions to accumulate both human and physical capital are heterogeneously
affected by inflation and, hence, factors reallocation takes place in inflation. This factors’
reallocation and the resulting accumulation of both human and physical capital explains
one possible channel behind the inflation-growth non-linearity (see also Gillman and
Kejak, 2005).
Theoretically, several possible mechanisms explain the interaction between inflation
and both types of capital accumulation. For example, on the human capital accumulation,
inflation can accelerate its accumulation by reducing the opportunity cost of schooling.
Since real wages fall in inflation, the accumulation of human capital becomes more
attractive for the young agents (Heylen and Pozzi, 2007). Conversely, the income effect of
inflation can force the agents to allocate more time to work and less to the human capital
development; causing a negative relationship between inflation and the human capital
accumulation (see Binder, 1999). Similarly, on the inflation and physical capital
accumulation relationship three competing possibilities have been advanced in literature.
First, Tobin (1965) observes a positive impact of inflation on the long-run physical capital
accumulation that, to him, results from real interest rate reduction following inflation (see
also Rapach and Wohar, 2005). Similarly, a higher inflation variability coming from
inflation can also stimulate the physical capital accumulation by increasing the
precautionary savings of agents (Dotsey and Sarte, 2000). Second, and exactly opposite to
1
Gillman et al. (2001) and Ghosh and Phillips (1998) also show how the adverse effects of additional inflation
decrease with increasing inflation rates, putting differently, the higher the level of inflation the lower the damage
it inflicts upon the long-run growth.
2
the first, inflation can reduce the accumulation of physical capital if agents substitute
consumption for investment. As increasing prices make money worth today than tomorrow,
consumption increases compared with savings. Accordingly, inflation induced disruptions
in the efficient functioning of the financial institutions also reduce the capital formation.
Third, Sidrauski (1967) posits no relationship between inflation and capital accumulation
by arguing that real and nominal variables move independently in the long-run. Lucas
(1980) empirically supports this view by finding no long-run relationship among M1,
interest rate and inflation for the U.S.
Interestingly, previous research indicates that these opposite effects of inflation on
factors’ realignment occur as inflation moves from its lower to higher levels. For example,
an overwhelming amount of theoretical literature indicates an adverse inflation-human
capital relationship supporting the presence of an income effect for the human capital
accumulation. Nonetheless, Heylen and Pozzi (2007) show that unexpected high
inflationary shocks stimulate the human capital development.2 The reverse is true for the
physical capital accumulation, here slight positive inflation rates are considered supportive
for the physical capital accumulation while high inflation reduces saving and investment.
This implies that a positive inflation-growth relationship in low inflationary environmentshown by the previous literature- can result from Tobin effect of inflation on the physical
capital accumulation. At a moderate inflation rate, accumulation of both types of capital
reduces and thus inflation-growth relationship becomes strongly negative. Finally, in
excessively high inflation periods, an increase in the accumulation of human capital can
partially offsets the negative inflation levels thus explaining a weak inflation effect in high
inflation periods.
In this paper, we empirically test these effects for a large panel data set of both
developed and developing countries. To the best of our knowledge this paper is the first
study to empirically investigate this possible mechanism behind the existing inflationgrowth non-linearity. More precisely, our paper tries to address few basic questions
concerning the inflation and capital accumulation relationship. First, we try to empirically
test whether inflation influences the behavior of agents in their accumulation of human and
physical capital. Second, we want to see whether this relationship remains linear in all
2
Theoretically all these positive effects of inflation on the accumulation of human capital usually depend upon
two assumptions; first, inflation is transitory phenomena and second, it is unpredictable for the agents. However,
there are more and more studies in the literature showing a long-run effect of inflation on the labor supply
decisions of the agents (see Graham and Snower, 2008).
3
ranges of inflation or there exist some thresholds which can explain the inflation-growth
non-linearity through factors’ accumulation. Third, which macroeconomic features of a
country shape the behavior of agents for their factors’ accumulation in inflation? For
instance, we try to investigate whether the depth of financial institutions and democracy
influence the nature and/or the sensitivity of this relationship. Finally, to test the theoretical
results of Dotsey and Sarte (2000) that a variable monetary policy and the resulting
variable inflation stimulate the capital accumulation, we analyze the effect of inflation
volatility on both human and physical capital accumulation.
Our main findings support a positive effect of inflation on the human capital
accumulation and an adverse effect for the accumulation of physical capital. Both these
effects are, nonetheless, non-linear and start appearing only when inflation crosses certain
thresholds. Moreover, supporting the theoretical claims of Dotsey and Sarte (2000), our
findings favor a variable monetary policy for the human capital accumulation, though not
for the accumulation of physical capital. Finally, all these relations are influenced by the
depth of financial institutions and strength of the democratic institutions in our selected
economies.
The remainder of this paper is organized as follows. Section 2 presents a very brief
summary of the theoretical and empirical advances in the analysis of the relationship
between inflation and capital accumulation. Section 3 describes the data set and the
econometric model used in the present study. Section 4 provides our main results and some
discussion. Finally, section 5 concludes.
2.
Theoretical Background
2.1.
Inflation and Physical capital accumulation
The exogenous growth models, starting from Solow (1956) assume saving as a constant
proportion of income and therefore ignore the role of money in the capital formation. Tobin
(1965) observes a substitution from money to physical capital due to lower real interest
rates in inflation, showing a positive impact of inflation on the physical capital
accumulation; a phenomenon that is named ‘Tobin effect’ in the subsequent literature.
Empirical literature supporting the Tobin effect include Ahmed and Rogers (2000) who use
a Vector Error Correction Model (VECM) for over 100 years of the U.S data to find a
positive impact of unanticipated inflationary shocks on consumption, investment and
output. Rapach (2003) and Rapach and Wohar (2005) indirectly support the Tobin effect by
4
showing a negative relationship between inflation and real interest rate. However, Gillman
and Kejak (2011) argue that a lower real interest rate compared with real wage can result
from agents’ preference for leisure. In this case a real interest rate reduction will not yield
higher investment. In Gillman and Kejak (2011), inflation causes an inter-temporal
substitution of consumption from current to future period while Gillman and Nakov (2003)
assume a substitution from labor to leisure; both these substitutions enhance the speed of
physical capital accumulation by increasing the real wages vis-à-vis the real interest rate.
Finally, in Overlapping Generation Model of Mino and Shibata (1995), inflation exerts
higher capital accumulation due to its redistributive effects from old to young generations.
Cheap availability of capital to young generation fastens its accumulation in inflation.
However, the cash-in-advance (C.I.A) model of Stockman (1981) supports an inverseTobin effect since inflation reduces the amount of cash available for the capital
accumulation. Walsh (1998) also criticizes Tobin for his Solow (1956) based exogenous
growth assumptions and the role of money being confined only to financial capital stocks.
Thus, according to Walsh (1998), the Tobin effect is temporary since inflation does not
increase the consumption and capital stock beyond the transition path; whereas the steady
state effects of inflation on the capital accumulation are negative. Fischer (1993)
empirically supports these results by showing a negative effect of inflation and inflation
volatility on the capital accumulation for 68 countries. A reversed Tobin effect is also
shown by the models where financial intermediation plays a role to channelize savings and
the capital accumulation (e.g., Ireland, 1994; Chari et al., 1996 and Haslag, 1998). In this
setup, inflation inhibits the capital accumulation by increasing the reserve requirements of
the financial institutions.
Notwithstanding the opposing theoretical views on the inflation and capital
accumulation relationship, the empirical investigation to this issue has not been conducted
sufficiently. As can be drawn from the above discussion, most of the previous work is
based on the country specific data- confined mainly to the U.S. This is at odd with the fact
that the need of the empirical work has been stressed since long by Summers (1981, p.193).
One apparent reason for this insufficient empirical treatment is unavailability of the data on
the capital accumulation as indicated by Crosby and Otto (2000; p.237, note 1). Their study
uses a structural VAR model to examine the relationship between inflation and the capital
accumulation for 34 countries and shows a non-robust relationship for a majority of the
selected economies.
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2.2.
Inflation and Human capital accumulation
The importance of human capital in the growth process has been highlighted since long
in the literature (e.g., Mincer, 1958). Accordingly, factors influencing its accumulation,
including inflation, have gained a considerable attention in the literature. However, most of
the previous studies assume complementarities between human and physical capital
accumulation and analyze a combine effect of inflation on both these factors.3 Wang and
Yip (1992), for example, present an endogenous growth model where money serves the
transaction purposes and then analyze the role of anticipated inflation on human and
physical capital accumulation. Their results show some insignificant effects of inflation on
both these factors of production. Pecorino (1995), however, opposes these results in a
model where physical capital works as an input in the production of human capital.
Inflation tax, under these conditions, reduces the demand for real balances and accordingly
the factors’ accumulation. In Gomme (1993), labor is used as an input for both production
and human capital accumulation under the assumption of free mobility of labor between
these two sectors. Inflation induced reduction of real wages in both sectors inhibit the speed
of human capital accumulation.
Several theoretical settings in the subsequent literature have complemented this
negative inflation and human capital accumulation relationship. The cash-in-advance (C-IA) model of Gillman and Nakov (2003) assumes substitution from work to leisure activities
in inflation which essentially reduces the accumulation of human capital. Gillman and
Kejak (2005) advance a model that nests several theoretical possibilities such as a physical
capital (AK) model, a human capital (AH) model and a combined model and show separate
effects of inflation in different cases. Generally, their findings support the conventional
view of the Tobin effect in the AK model, the anti-Tobin effect in the AH model and
parallel results for the combine model.
Nevertheless, the Overlapping Generations Models (OLG) show a positive effect of
inflation on the human capital accumulation due to its redistribution effects between old
and young generations (Bhattacharya and Haslag, 2001). Here inflation reduces the net
savings of the old generation and the net borrowing of the young generation. This
redistribution enables the later group to enhance their learning and, hence, fosters the
3
This joint treatment of both factors of production is theoretically motivated by Nelson and Phelps (1966);
Romer (1993) and empirically tested by Grier (2002, 2005).
6
human capital formation. This view has also been supported by some empirical country
specific studies where the process of human capital development is shown to be positively
affected by high inflation episodes (see Duryea and Arends-Kuenning, 2003 for Brazil).
Surprisingly, despite these plausible links between inflation and human capital
accumulation advanced by a variety of models, empirical literature on the subject is again
very sparse. Exceptions include two recent studies by Heylen and Pozzi (2007) and
Yilmazkuday (2013). Heylen and Pozzi (2007) test the impact of high inflation episodes on
the accumulation of human capital for a panel of 86 countries and confirm a positive
impact of inflation crisis on the human capital development. Nevertheless, the study is
confined to high inflation episodes only and thus overlooks the overall relationship
between these variables at different inflation rates. Besides, Yilmazkuday (2013) analyzes
how inflation influences the contribution of different macroeconomic features- including
the human capital accumulation- to growth and finds a 15% threshold inflation rate for a
positive effect of human capital accumulation on growth.
2.3.
Country specific characteristics and inflation-capital accumulation nexus
All the above mentioned effects of inflation on the capital accumulation can also be
influenced by some specific macroeconomic features of an economy. More precisely, the
direct inflation and capital accumulation relationship can be appeased or intensified by
some country-specific characteristics that affect the agents’ decisions for the accumulation
of both human and physical capital, as indicated by the previous literature. For instance, if
inflation obstructs the signaling channel of price changes (Lucas, 1973), increases the user
cost of capital (Madsen, 2003; Byrne and Devis, 2004) and reduces the real savings of the
agents (Stockman, 1981), its reversed Tobin effect on the accumulation of physical capital
should be less severe in strong financial systems. The direct positive effects of financial
development modify the adverse inflation effects on the physical capital accumulation.
Indeed, a strong financial system of a country help the entrepreneurs in their investment
decisions, improves the monitoring of different projects and develops corporate governance
(Cesar and Liu, 2003). Similarly, a well developed financial system also enables the agents
to improve their human capital in inflation by providing them loans for consumption and
human capital accumulation purposes. Inflation induced lower real wages can favor the
skill acquisition when financial institutions extend sufficient resources for this purpose
(Becker, 1975; Harris and Sakellaris, 2003). In short, a sound financial system is a
prerequisite for the desirable effects of inflation on human and physical capital
accumulation.
7
Similarly, the inflation effects on the physical and human capital accumulation also
depend upon the domestic political institutions. As strong political institutions ensure
property rights of the agents for their innovations and physical assets, they ultimately favor
the accumulation of both types of capital accumulation. Clague et al. (1996) particularly
support this argument for the physical capital accumulation where they find a positive
impact of long-lasting democracies on the accumulation of physical capital. Kurzman et al.
(2002) argue that democratic regimes increase the investment opportunities and therefore
foster the physical capital accumulation. An opposing view states that the political process
redistributes resources between capital and labor that may favor the later by safeguarding
the labor interests and strengthening the unions. Tavares and Wacziarg (2001) support this
view for 65 countries by showing a negative effect of democracy on the physical capital
and a positive effect on the human capital accumulation. The direct positive link between
democracy and human capital accumulation has also been shown by Grier (2005). Along
the same lines, the literature that investigates the indirect channels of the democracy’s
effects on growth also shows that the human capital accumulation is the main channel
through which democracy enhances the long-run growth (see Barro, 1996; Wacziarg,
1999).
However, the evidence on the relationship between democracy and inflation is not
concrete. One view states that inflation is usually high in autocratic regimes due to the rent
seeking behavior of the ruling classes and it decreases with democratization of an economy
(Bates and Kruegger, 1993; Shanker and Subramanian, 2007). On the other hand, populist
approach to democracy states that a democratic regime has to meet public demands and
therefore it imposes inflation tax to finance its large public size (Nelson, 1993). In Desai et
al. (2003) democratic regimes suffering from unequal income distribution generate
revenues through inflationary taxes for re-distributional purposes. Finally, there exists
some literature supporting a lack of robust relationship between inflation and political
regimes (e.g., Mijiyawa, 2011). All these perplexing theoretical and empirical evidences on
the tripartite democracy, inflation and capital accumulation relationship motivates us to test
whether the inflation effects on both human and physical capital accumulation depend upon
the institutional quality of that country.
3.
Data and Empirical Approach
8
Our empirical analysis is based on annual data of 104 countries over the period 19712010.4 To remove the business cycle effects and measurement errors from our estimated
results, five-year average data has been used. As we have several missing observations for
our main variables, our dataset can be denoted as ‘unbalanced panel’ and therefore we
never had complete 104 countries in our econometric specifications. Human and physical
capital accumulation variables are taken as dependent variables in the analysis. On the
control variables, GDP growth of a country directly impacts the capital accumulation as
high growth generates surplus income to invest in the capital stock (Keynes consumption
theory). By contrast, high population growth reduces the existing stock of capital per
worker (Solow, 1956). Our next covariate democracy is expected to positively affect the
capital stock. Besides, financial development, public size and government expenditures on
education are also taken as control variables in the physical and human capital
accumulation models respectively. Finally, as the previous literature indicates a joint
determination of both types of capital accumulation, the physical capital accumulation
variable is included in the equation of human capital accumulation and vice versa (Grier,
2005). Table (4) in the appendix (A) shows the main descriptive statistics of all these
variables.
Our panel equations for the human and physical capital accumulation can be expressed
as:
Hit  0  1 it  2 Zit   it
(1)
Kit  0  1 it  2 Zit   it
(2)
4
Data sources and calculations are given in Appendix A. Selected sample includes Algeria, Argentina, Australia,
Austria, Bangladesh, Barbados, Belgium, Benin, Bolivia, Botswana, Brazil, Burkina Faso, Burundi, Cameroon,
Canada, Central African Republic, Chad, Chile, China, Colombia, Congo. Dem. Rep., Congo. Rep., Costa Rica,
Cote d'Ivoire, Denmark, Dominican Republic, Ecuador, Egypt. Arab Rep., El Salvador, Fiji, Finland, France,
Gabon, Gambia. The, Germany, Ghana, Greece, Guatemala, Guyana, Haiti, Honduras, Hong Kong. China,
Hungary, Iceland, India, Indonesia, Iran. Islamic Rep., Ireland, Israel, Italy, Jamaica, Japan, Kenya, Korea. Rep.,
Kuwait, Lesotho, Libya, Luxembourg, Madagascar, Malawi, Malaysia, Mali, Malta, Mauritania, Mexico,
Morocco, Myanmar, Nepal, Netherlands, New Zealand, Nicaragua, Niger, Nigeria, Norway, Oman, Pakistan,
Papua New Guinea, Paraguay, Peru, Philippines, Portugal, Rwanda, Saudi Arabia, Senegal, Sierra Leone,
Singapore, South Africa, Spain, Sri Lanka, Sudan, Swaziland, Sweden, Switzerland, Syrian Arab Republic,
Thailand, Togo, Trinidad and Tobago, Tunisia, Turkey, United Kingdom, United States, Uruguay, Venezuela.
RB, Zambia.
9
Equation (1) is the human capital accumulation model where Δ𝐻𝑖𝑡 represents a change
in the five year average human capital stock and 𝜋𝑖𝑡 stands for inflation. The vector 𝑍𝑖𝑡
includes all above mentioned control variables. As the vector 𝑍𝑖𝑡 contains physical capital
accumulation in equation (1), the joint determination of both types of capital (see Grier,
2005) violates the orthogonality condition E(Kit  it )  0 and as a consequence ordinary
least square (OLS) will yield biased and inconsistent coefficient estimates. Same applies to
equation (2) for the physical capital accumulation. Our response to these problems with
OLS is estimating both equations using the fixed effects model by incorporating time and
county specific effects in the above models. The modified equations take the following
forms:
Hit  0  1 it  2 Zit  i  t   it
(3)
Kit  0  1 it  2 Zit  i  t   it
(4)
The last two parameters 𝛼𝑖 and 𝜆𝑡 represent country and time fixed effects respectively.
Alternatively for the robustness purposes the aforementioned unobserved heterogeneity
problem is also treated by using an instrumental variables (i.e., two-stage least squares)
model with initial values of the control variables for each 5-year period serving as
instruments in the first stage. Wooldridge (2001) shows that both the fixed effects and 2SLS models give consistent results since the fixed effects transformation essentially
incorporates the possible sources of endogeneity such as unobserved heterogeneity and
simultaneity bias.
So far we have assumed a linear functional form of the relationship between inflation
and capital accumulation. Nevertheless, the nature of the precise functional form is an
important issue since it has some important bearings on the optimal inflation rate for the
capital accumulation. To address these issues, we first conduct a preliminary test with an
additional interaction variable of inflation square in equations (1) and (2). The objective is
to see whether, beyond certain thresholds, inflation becomes more or less important in
influencing the capital accumulation. To illustrate, with the additional inflation square
term, equation (3) becomes:
H it   0  1 it   2 it2   3 Zit  i  t   it
10
(5)
The inclusion of this interaction term allows us to estimate the marginal effects of
inflation on the capital accumulation at different inflation rates. These marginal effects can
be calculated by examining the partial derivative of Δ𝐻𝑖𝑡 with respect to 𝜋𝑖𝑡 :
 (H it )
 1  2 2 it
 it
(6)
Evidently, the marginal effect for a one unit change in inflation depends not only on 1
and  2 but also on the value of 𝜋𝑖𝑡 . The non-linearity in the physical capital accumulation
is treated accordingly.
Second, for a more continuous and robust investigation of this non-linearity in the
inflation and capital accumulation relationship, a rolling regression technique has been
adopted. The main advantage of this method is that it shows the behavior of inflation
coefficients with increasing inflation rate and hence is considered a smooth method to
analyze the non-linearity (see Rousseau and Watchel, 2002 and Yilmazkuday, 2011 for a
more detailed discussion). To conduct this analysis, all the observations in the dataset are
arranged in ascending order of inflation rate and then a constant window of 150
observations is employed to get the inflation coefficients.
Similarly, to analyze the role of macroeconomic conditions, an interaction term is
included in the above models and the resulting equations become:
Hit  0  1 it  2 Zit  3 it X it  i  t   it
(7)
Kit  0  1 it  2 Zit  3 it X it  i  t   it
(8)
The interaction variable 𝑋𝑖𝑡 represents financial development and democracy in both
equations.
4.
Results and Discussion
Table 1 presents our main results that have been obtained by using both fixed effects
and instrumental variable-2SLS models. Specification (1) shows a negative and significant
effect of inflation on the physical capital supporting an overall reverse Tobin effect on its
accumulation. These negative effects are consistent with the previous literature that has shown
the adverse effects of uncertain macroeconomic environment on the investment decisions of
11
the firms (Fischer, 1993). Madsen (2003) argues that inflation increases the nominal interest
rate and reduces the accounting profits of the liquidity constrained firms which, consequently,
results in lower savings and capital formation. Moreover, the author posits that inflation
increases the user cost of capital by reducing the real value of tax depreciation that are
recorded at the initial price of capital stock. The positive sign of democracy variable
highlights the importance of democratic regimes in assuring transparency, securing property
rights and thus enhancing the capital accumulation. Next, a strong financial system is found to
have a positive influence on the capital accumulation through better credit allocation and risk
management. Specification (2) reproduces the same results in instrumental variable 2-SLS
framework. Here, beside the other covariates, GDP growth is significant showing the validity
of Keynes consumption theory for the physical capital accumulation.
Table (1): Human and Physical Capital Accumulation regressions, 1971-2010
(1)
(2)
(3)
(4)
(5)
(6)
VARIABLES
Physical
Physical
Human
Human Secondary Secondary
Capital
Capital
Captial
Captial Education Education
F.E
2-SLS
F.E
2-SLS
F.E
2-SLS
Human Capital
-0.057
(0.504)
-0.195
(0.385)
Physical Capital
Inflation
Democracy
Financial Dev.
GDP Growth
-3.547**
(1.610)
8.614*
(5.056)
0.163***
(0.056)
0.030
(0.024)
Population Growth
Education Exp.
Constant
29.725***
(8.284)
-2.357*
(1.429)
0.014
(0.357)
0.114*
(0.063)
0.951**
(0.373)
-0.117
(0.658)
0.111**
(0.052)
0.019*
(0.011)
0.014**
(0.007)
0.064*
(0.033)
0.112
(0.106)
0.009**
(0.005)
0.010*
(0.005)
0.052*
(0.031)
0.012*
(0.007)
0.098***
(0.037)
-0.032
(0.115)
0.000
(0.000)
0.011
(0.015)
-0.011
(0.040)
-2.018***
(0.265)
0.001
(0.012)
0.091**
(0.037)
-2.015***
(0.142)
Observations
468
340
524
671
661
R-squared
0.115
0.140
0.378
0.349
0.571
No. of Countries
87
63
78
89
85
Standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1
405
0.431
78
Our next model (specification 3) shows a positive impact of inflation on the human
capital accumulation. This supports the substitution effect hypothesis where the lower real
12
wages or the lower opportunity cost of education motivates the agents to acquire new skills
during the inflationary periods (Heylen and Pozzi, 2007). Reduced employment
perspectives in inflation can also lead to higher human capital accumulation if the agents
are optimistic about the future stable economic environment. That said both democracy and
financial development variables take the hypothesized positive signs. As democracy is
considered to be more responsive to the public demands, it allocates more resources for
education (see Barro, 1996). Accordingly, financial development facilitates the provision of
funds to the young agents for their skill acquisition purposes and therefore exerts positive
impact on the accumulation of human capital- as shown by the positive coefficient.
Specification 4 provides the same results in 2-SLS framework.
In the last two specifications (5 and 6) we have tested the robustness of our findings
with respect to the level of education. Here we take secondary mean years of schooling from
the same data stream (Appendix A). Indeed, as shown by Barro (1999), the secondary or
higher levels of education are more significant in the growth regressions (see also Heylen
and Pozzi, 2007). More importantly, this alternative measure of human capital accumulation
is also interesting for our particular question as the substitution between work and human
capital accumulation- during inflation- is more easier at secondary or higher level of
education. Our results concerning the positive effects of inflation are in line with the
primary education findings. One additional result is the positive effect of physical capital
accumulation to enhance the secondary education. These capital-skill complementarities
come from the fact that the higher physical capital increases the wage premium of skilled
workers and therefore stimulates investment in human capital. Finally, government
spending on education appears with positive sign, as expected. The results on tertiary
education-not show here for brevity- follow the same pattern.
Indeed, it is not only the average level of inflation that influences the capital
accumulation but also higher inflation variability that is positively associated with it (Lucas,
1973). Fischer (1993) posits that inflation uncertainty causes budget or current account
instability which consequently reduces the capital stock and productivity. Dixit and Pindyck
(1993) argue that inflation induced uncertainty halts the investment projects and its impact
can be even larger than the direct interest rate effects. In contrast, Dotsey and Sarte (2000)
explain a positive impact of uncertainty on the capital accumulation. To authors, the effect
of monetary policy variability and the resulting inflation volatility is positive on the capital
accumulation and growth though the effects of average inflation are negative. These
13
conflicting results motivate us to test the effects of inflation volatility on the capital
accumulation. To do this, we have generated an inflation uncertainty variable from quarterly
inflation data (see appendix A) and then tested its effects on both human and physical
capital accumulation.
Table (2): Human and Physical Capital Accumulation regressions, 1971-2010
(1)
(2)
(3)
(4)
(5)
(6)
VARIABLES
Physical
Physical
Human
Human
Physical
Human
Capital
Capital
Captial
Captial
Capital
Capital
F.E
2-SLS
F.E
2-SLS
F.E
F.E
Human Capital
0.744
(7.964)
2.119
(8.104)
0.250
(0.814)
Physical Capital
Inflation Volatility
Democracy
Financial Dev.
-0.869***
(0.150)
14.661**
(5.692)
0.253***
(0.065)
-0.887***
(0.150)
9.139*
(4.764)
0.172***
(0.059)
Government Exp.
-0.012*
(0.007)
Population Growth
Inflation
Inflation Square
Constant
0.009
(0.006)
0.004
(0.002)
0.013*
(0.007)
18.253***
(5.470)
0.073***
(0.022)
0.014*
(0.008)
1.219***
(0.413)
-0.001
(0.008)
-0.066*
(0.034)
-0.118*
(0.060)
-0.001
(0.002)
0.003
(0.003)
0.282**
(0.141)
-0.658**
(0.330)
0.004
(0.003)
9.520**
-0.044*
(4.204)
(0.025)
-2.250*** 0.008*
(0.794)
(0.004)
-4.239
0.259***
(10.215)
(0.056)
Observations
516
508
581
483
514
R-squared
0.202
0.192
0.378
0.088
0.144
No of Countries
78
78
79
78
84
Standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1
450
0.067
74
Table 2 shows some interesting results on the link between inflation volatility and the
accumulation of human and physical capital. The first two specifications show a negative
effect of inflation volatility on the physical capital consistent with the previous research
(Fischer, 1993; Grier, 2005). These results validate the concerns raised by the misperception
theory that one important channel through which inflation reduces the capital accumulation
is through nominal uncertainty. The next two specifications show a positive impact of
inflation uncertainty on the human capital accumulation, though significant only in the
14
second case. Heylen and Pozzi (2007) conjecture that though the uncertain environment
reduces the return to work and physical capital stock, its impact on human capital
accumulation is positive. Agents work less and study more which stimulates the human
capital accumulation. Next, government expenditures variable appears with negative sign
showing the inefficiency of public finance for both types of capital accumulation. All other
covariates retain the same signs and significance as they appear in Table 1.
So far we have assumed a linear relationship between inflation and capital
accumulation. This is not necessarily the true functional form as behavior of the agents can
be different when inflation moves from its lower to higher regimes. In the last two
specifications of Table 2, we address the non-linearity between inflation and capital
accumulation by estimating equation 3 of the model. Here our additional variable, inflation
square, is significant in both cases showing the existence of inflexion point in the inflation
effects on human and physical capital accumulation. Interestingly, for the physical capital
accumulation the inflation parameter is positive while the inflation square parameter is
negative which states that the previous adverse effects of inflation are only valid when it
crosses certain threshold point. The threshold value estimated by using equation 4 is
 *  2.11% , inflation below this level exerts Tobin effects on the physical capital whereas
above this level it reduces the capital accumulation. For the human capital accumulation the
estimated threshold is  *  2.75% with the inflation effects being negative below this level
and positive afterward. These findings support our previous results that high inflation
uncertainty discourages the physical capital accumulation but not the human capital
accumulation. The negative sign on population growth variable explains lower per-capita
capital stock in high population growth countries consistent with the Solow growth model
(Mankiw et al. 1992).
Besides, for a more robust and continuous analysis of this non-linear relationship, we
used a rolling regression model. Our results for the inflation threshold using the rolling
regression technique are presented in Figure 1. In the first part (Figure 1.a); the effect of
inflation on physical capital accumulation has been tested with the observations of
increasing inflation. As the graph shows, the effect of inflation is positive and significant in
low inflation regimes supporting the Tobin’s view concerning the inflation effects on the
physical capital accumulation. However, when inflation crosses 2.7%, the Tobin effect turns
into reverse Tobin effect and remains so afterward. Figure 1.b shows an ambiguous behavior
of inflation coefficients for the human capital accumulation. Here the inflation effect is
mostly negative other than some middle range coefficients as well as high inflation
15
coefficients when it crosses 4%.
.1
-.1
-200
0
-100
0
R-Squared
.2
100
.3
200
a)
1
2
3
4
5
1
Inflation
_b[Inflation]
3
4
5
Inflation
lower/upper
.4
0
-100
-50
.2
0
50
R-Squared
100
.6
150
b)
2
1
2
3
4
1
5
_b[Inflation]
2
3
4
Inflation
Inflation
lower/upper
Figure 1. a) Inflation effects on physical capital b) Inflation effects on human capital
Certainly these direct inflation effects on the human and physical capital accumulation
are not the same for economies working under different macroeconomic environment. To
analyze the role of some theoretically justified conditional variables, we have tested
equations (7) and (8) with two interaction variables e.g., financial development and
democracy and the results are presented in Table 4. Specification (1) in Table 4 shows a
weak reversed-Tobin effect of a given inflation rate in strong financial systems. Obviously,
as discussed in section (2.3), the undesirable inflation effects on the physical capital
accumulation should be lower for a country with a well developed financial system since the
efficient functioning of the financial institutions nullifies the direct inflation effects on the
physical capital accumulation. In fact the value of the inflation parameter explains its stand
alone when financial development is zero. This reversed Tobin effect of inflation becomes
weaker at higher values of the modifying variable- the financial development.
16
5
Similarly, specification (2) explains the moderating role of financial development for
the inflation-human capital accumulation nexus. Here, again, the developed financial
systems facilitate the agents for their decisions to accumulate human capital in inflationary
periods. The direct inflation coefficient is, however, insignificant. In the next specification
we analyze whether the adverse inflation effects on the physical capital accumulation are
moderated by the democratic regimes. Our results favor the hypothesis that the adverse
inflation effects are less severe in the democratic regimes. As the democratic regimes ensure
transparency and property rights, investment in the new projects becomes easier in these
regimes. This to some extent modifies the reversed Tobin effects. Finally, specification (4)
tests the possibility of regimes dependence for the desirable inflation effects on the human
capital accumulation. Here, the positive inflation effects on the human capital accumulation
are weak in the presence of strong democratic institutions. This may appear from the fact
that in strong democracies, central bank independence may not leave inflation to enter into a
zone where the agents substitute the human capital accumulation with work. On the whole,
the strong financial institutions speed-up the accumulation of both human and physical
capital while democracy only moderates the adverse inflation effects on the accumulation of
physical capital. Given that all these interaction variables are continuous, the net impact of
the modifying variables and their statistical significance cannot be directly judged based on
the coefficients. To get some more precise results, we followed Brambor et al. (2006) and
estimated the marginal effects of inflation on the capital accumulation conditional upon
these macroeconomic characteristics.
The Figure 2.a shows that the reverse Tobin effect of inflation on the physical capital
accumulation is strongly dependent upon the level of financial development in an economy.
The results with 90% confidence interval show that the negative effect disappears for
economies with M3/GDP ratio higher than 35%. More interestingly, same level of inflation
yields a Tobin effect for economies with M3/GDP ratio higher than 200%. Stated
differently, the marginal effects of inflation on the physical capital are negative for M3/GDP
< 35%, insignificant for 35% < M3/GDP < 200% and positive afterwards. Similarly, in
Figure 2.b financial development strongly support the accumulation of human capital for
M3/GDP > 30%. Here, although the effects remain positive throughout the range of
financial development variable, the positive effects become insignificant in weak financial
systems.
17
Table (3): Human and Physical Capital Accumulation regressions, 1971-2010
(1)
(2)
(3)
(4)
VARIABLES
Physical
Human
Physical
Human
Capital
Capital
Capital
Capital
Human Capital
0.326
(0.623)
Physical Capital
Inflation
0.010*
(0.006)
0.024
(0.060)
-0.005**
(0.003)
0.002*
(0.001)
-5.381**
(2.504)
0.129
(0.126)
0.079**
(0.039)
Financial Development
Inflation*Financial Dev.
Democracy
Inflation*Democracy
Public Expenditures
-0.881**
(0.366)
41.184***
(8.975)
Constant
-3.884*
(2.087)
0.122***
(0.041)
0.093
(0.431)
1.310***
(0.476)
0.005
(0.008)
-0.015*
(0.009)
6.705*
(3.891)
0.223***
(0.081)
-2.098***
(0.238)
Observations
600
506
435
R-squared
0.129
0.546
0.061
No. of Countries
86
76
Standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1
Figure (2.a)
Inflation Effects on Physical Capital As Financial Development Changes
-8.86739
32.39709
Dependent Variable: Physical Capital
0
50
100
150
200
250
300
Financial Development
Marginal Effect of Inflation
90% Confidence Interval
Figure (2.b)
Inflation Effects on Human Capital As Financial Development Changes
-.0603311
.9130108
Dependent Variable: Physical Capital
0
50
100
150
200
Financial Development
18
Marginal Effect of Inflation
90% Confidence Interval
250
300
524
0.549
Inflation Effects on Physical Capital As Democracy Changes
Figure (2.c)
-26.54196
16.63503
Dependent Variable: Human Capital
-10
-5
0
5
10
Democracy
Marginal Effect of Inflation
90% Confidence Interval
Figure (2.d)
Inflation Effects on Human Capital As Democracy Changes
-.1778497
.4527453
Dependent Variable: Human Capital
-10
-5
0
5
10
Democracy
Marginal Effect of Inflation
90% Confidence Interval
Figure (2): Macroeconomic Developments and inflation-capital accumulation nexus
In the next two parts of the Figure, 2.c and 2.d, the moderating role of democracy on the
accumulation of both human and physical capital is analyzed. Consistent with the previous
findings of the physical capital variables, the reverse Tobin effect of inflation is relevant only
for the democratic regimes; as shown by Figure 2.c. For the same inflation level, a change in
inflation can lead to a reverse Tobin effect in autocratic regimes and a Tobin effect in
democracy. The Figure 2.d the results are slightly different; as discussed earlier. Here, in
strong democratic regimes inflation does not influence the agents’ human capital
accumulation decision. The overall results indicate that the reverse Tobin effect for physical
capital is sensitive to the country specific macroeconomic conditions such as the financial
development and democracy while the desirable effects of inflation on the human capital are
dependent require strong financial system.
5. Conclusions and policy implications
A bulk of recent literature has identified non-linearity in the long-run inflation-growth
relationship. The literature also finds that the intensity of these adverse inflation effects on
growth reduces at increasing inflation rates. Gillman and Nakov (2003) argue that this
dynamic response of output to inflation changes reflects the factors’ realignment and their
19
accumulation in inflation. Our paper brings some empirical substantiation to this view and
probes into the existence of ‘Tobin effect’ and several other theoretical possibilities in a large
panel data of developed and emerging economies.
Our main results confirm the reverse Tobin effects for the accumulation of physical capital
and a substitution effect (from work to education) for the human capital accumulation. These
findings are consistent with the theoretical results of Gillman and Kejak (2005). However,
both these effects are non-linear and are relevant only when inflation crosses certain threshold
points. In other words, after certain inflation level, it discourages the accumulation of human
capital and encourages the accumulation of physical capital. These findings explain one
plausible channel behind the inflation-growth non-linearity.
Our empirical results imply that the adverse effects of any level of inflation are country
specific and depend upon the factor endowments of that economy. As the role of inflation tax
is significantly different in countries with heterogeneous factors endowments, production
technologies and institutional arrangements, any policy to curb inflation in an economy must
take into account these country specific characteristics of that economy. The welfare
implications of the same level of inflation can differ across countries with these structural
differences. A more clear distinction is made when we study some macroeconomic
developments, possibly influential for this relationship. Here we find the existence of Tobin
effect of inflation on the physical capital accumulation for economies with strong financial
and political institutions. For democratic and financially developed economies, the direct
negative effects of inflation on the physical capital accumulation become positive as the
financial and democratic institutions create an investment friendly environment that helps the
investors in making their investment decisions. Similarly, the strong financial institutions are
also helpful in making substitution from work to human capital accumulation in inflation.
Next, on the role of political regime, even if the task of controlling inflation becomes
harder in some populist governments, its welfare implications on the long-run growth are not
alarmingly severe due to a rapid accumulation of physical capital in these countries. However,
this certainly does not suggest the use of seigniorage tax in a democratic regime as its other
undesirable effects i.e on relative-price-variability and the resulting resource misallocation
start appearing from a very low level of inflation. To end, two points need to be re-asserted,
first although our estimated results do not contain any direct message for the optimal inflation
rate, they enable us to understand the empirical inflation-growth non-linearity advanced by
20
the previous literature. Second our empirical results also suggest that the existing empirical
inflation-growth literature has emerged in a closed environment and consequently it overlooks
some important dimensions of inflation effects. At best, these findings, along with some other
results of the recent literature (see Ylimazkuday, 2012) state that the optimal inflation rate
depends upon several macroeconomic developments and institutional qualities of a country
and hence the optimal inflation rate changes with these dynamics.
Appendix A: Descriptive Statistics, Data Definitions and Sources
Definition of the variables and Data sources
Primary
Education
Secondary
Education
Physical
Capital
Π5yt
VINF5yt
GE5yt
DEMOC5yt
Pop.Gr5yt
Gov.Exp5yt
Fin. Dev5yt
GDP.Gr5yt
Average years of primary schooling for the population of age 15 and older taken
from Barro and Lee (2010). First difference yields the required variable.
Average years of secondary schooling for the population of age 15 and older
taken from Barro and Lee (2010). First difference yields the required variable.
Indicator of physical capital accumulation has been retrieved from Penn-World
Tables 7.1.
Average annual changes in the log values of consumer price inflation (п) in the
period of 5 years before t, taken from the World Development Indicators (WDI,
online data bank).
Inflation variability is calculated by 5-years standard deviation of inflation from
quarterly observations taken from International Financial Statistics CD-ROM
(IFS, 2011). Ten windows of 20 observations each (1971Q1-1975Q4) are
generated and then inflation variability is calculated as VINF=log(1+sd(INF)).
Average annual real per capita government expenditures on education (as
percentage of real GDP) in the five year before t. This data set has been obtained
from
UNESCO
online
data
source:
http://www.uis.unesco.org/i_pages/IndPGNP.asp.
Indicator of democracy varies from -10 (highly autocratic) to 10 (highly
democratic). Polity IV, source http://www.systemicpeace.org/polity/polity4.htm.
Average annual population growth data is retrieved from the World Development
Indicators (WDI).
Average annual government expenditure as proportion of GDP data is obtained
from the World Development Indicators (WDI).
Ratio of liquid liabilities (M3) to GDP is taken as an indicator of financial
development.
The effect of GDP growth on the accumulation of physical and human capital
accumulation is controlled by including the 5-years average GDP growth.
21
Table (4): Descriptive Statistics
Variable
Mean
Std. Dev
Minimum
Maximum
Physical Capital
Primary Education
Secondary Education
Inflation
GDP Growth
Population Growth
M3/GDP
Public Size
Education Expenditure
8.374
0.028
0.029
0.138
3.383
1.919
47.351
15.578
3.841
33.472
0.901
0.812
0.293
48.853
2.426
35.449
6.523
1.598
-200.698
-4.932
-5.571
-0.042
-12.105
-6.222
6.276
14.134
0.356
184.505
3.783
1.873
4.192
14.18
6.889
280.211
86.597
10.051
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