WPS A 13
POLICY RESEARCH WORKING PAPER 2913
Financial Development
and Dynamic Investment Behavior
Evidence from Panel Vector Autoregression
Inessa Love
Lea Zicchino
The World Bank
Development Research Group
Finance
October 2002
POLIcy RESEARCH WORKING PAPER 2913
Abstract
Love and Zicchino apply vector autoregression to firm- availability of internal finance) that influence the level of
level panel data from 36 countries to study the dynamic investment. The authors find that the impact of the
relationship between firms' financial conditions and financial factors on investment, which they interpret as
investment. They argue that by using orthogonalized evidence of financing constraints, is significantly larger in
impulse-response functions they are able to separate the countries with less developed financial systems. The
"fundamental factors" (such as marginal profitability of finding emphasizes the role of financial development in
investment) from the "financial factors" (such as improving capital allocation and growth.
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at ilove@worldbank.org or lea.zicchino@bankofengland.co.uk. October 2002. (32 pages)
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Produced by the Research Advisory Staff
Financial Development and Dynamic Investment
Behavior: Evidence From Panel Vector
Autoregression.
Inessa Love and Lea Zicchinol
lInessa Love is at the World Bank, Research Department - Finance Group, 1818 H St.,
NW, MC3-300, Washington, DC, 20433. Email: ilove@worldbank.org. Lea Zicchino is at
the Bank of England, Financial Industry and Regulation Division, HO-3, Threadneedle
Street, London EC2R 8AH, UK. Email: lea.zicchino(bankofengland.co.uk. The paper was
completed while Lea Zicchino was at Columbia University, New York.
1 Introduction
Unlike the neoclassical theory of investment, the literature based on asymmetric in-
formation emphasizes the role played by moral hazard and adverse selection problems
in a firm's decision to invest in physical and human capital. As a result, the classical
dichotomy between real and financial variables breaks down. In other words, financial
variables can have an impact on real variables, such as the level of investment and the
real interest rate, as well as propagate and amplify exogenous shocks to the economy.
For example, Bernanke and Gertler (1989) show that a firm's net worth (a finan-
cial variable) can be used as collateral in order to reduce the agency cost associated
with the presence of asymmetric information between lenders and borrowers. In this
model, the firms' investment decisions are not only dependent on the present value of
future marginal productivity of capital, as the q-theory approach predicts, but also
on the level of collateral available to the firms when they enter a loan contract.
Since economists started to look at real phenomena abstracting from the Arrow-
Debreu framework with its frictionless capital markets, a vast literature has been
developed on the relationship between investment decisions and firms' financing con-
straints (see Hubbard, 1998, for a review). Even though asymmetric information
between borrowers and lenders may be not the only source of imperfection in the
credit markets, it remains a fact that firms seem to prefer internal to external finance
to fund their investments. This observation leads to the prediction of a positive re-
lationship between investment and internal finance. The first study on panel data
by Fazzari, Hubbard and Peterson (1988) found that after controlling for investment
1
opportunities with Tobin's q, changes in net worth affect investment more in firms
with higher costs of external financing.
The link between the cost of external financing and investment decisions not
only sheds light on the dynamics of business cycles but also represents an important
element in understanding economic development and growth. For instance, in the
presence of moral hazard in the credit market, firms that do not have internal funds
and need to get a bank loan may be induced to undertake risky investment projects
with low expected marginal productivity. This corporate decision affects the growth
path of the economy, which may even get stuck in a poverty trap (see Zicchino,
2001). Recently, Rajan and Zingales (1998), Demirguc-Kunt and Maksimovic (1998)
and Wurgler (2000) have looked at the link between finance and growth and have
examined whether underdeveloped legal and financial systems could prevent firms
from investing in potentially profitable growth opportunities. Their empirical results
show that active stock market, developed financial intermediaries and the respect of
legal norms are determinants of economic growth.
Estimation of the relationship between investment and financial variables is chal-
lenging because it is difficult for an econometrician to observe firms' net worth and
investment opportunities. In theory, the measure of investment opportunities is the
present value of expected future profits from additional capital investment, or what
is commonly called marginal q. This is the shadow value of an additional unit of
capital and it can be shown to be a sufficient statistic for investment. This is the
'fundamental' factor that determines investment policy of profit-optimizing firms in
2
efficient markets. The difficulty in measuring marginal q, which is not observable,
results in low explanatory power of the q-models and, typically, entails implausible
estimates of the adjustment cost parameters.1
Another challenge is finding an appropriate measure for the 'financial' factors that
enter into the investment equation in models with capital markets imperfections (such
as adverse selection and moral hazard). A widely used measure for the availability
of internal funds is cash flow (current revenues less expenses and taxes, scaled by
capital). However, cash flow is likely to be correlated with the future profitability
of the investment.2 This makes it difficult to distinguish the response of investment
to the 'fundamental' factors, such as marginal profitability of capital, and 'financial'
factors, such as net worth (see Gilchrist and Himmelberg (1995 and 1998) for further
discussion of this terminology).
In this paper we use the vector autoregression (VAR) approach to overcome this
problem and isolate the response of investment to financial and fundamental factors.
Specifically, we focus on the orthogonalized impulse-response functions, which show
the response of one variable of interest (i.e. investment) to an orthogonal shock in
another variable of interest (i.e. marginal productivity or a financial variable). By
orthogonalizing the response we are able to identify the effect of one shock at a time,
while holding other shocks constant.
'See Whited (1998) and Erikson and Whited (2000) for a discussion of the measurement errors in
investment models. Also see Schiantarelli (1996) and Hubbard (1998) for a review on methodological
issues related to investment models with financial contraints.
2For example, the current realization of cash flow would proxy for future investment opportunities
if the productivity shocks were positively serially correlated.
3
We use firm-level panel data from 36 countries to study the dynamic relationship
between firms' financial conditions and investment levels. Our main interest is to
study whether the dynamics of investment are different across countries with differ-
ent levels of development of financial markets. We argue that the level of financial
development in a country can be used as an indication of the different degrees of fi-
nancing constraints faced by the firms. After controlling for the 'fundamental' factors,
we interpret the response of investment to 'financial' factors as evidence of financing
constraints and we expect this response to be larger in countries with lower levels
of financial development. To test this hypothesis we divide our data in two groups
according to the degree of financial development of the country in which they oper-
ate. We document significant differences in the response of investment to 'financial'
factors for the two groups of countries.
We believe our paper contributes to the literature on financial constraints and
investment in several ways. First, by using vector autoregressions on panel data
we are able to consider the complex relationship between investment opportunities
and the financial situation of the firms, while allowing for a firm-specific unobserved
heterogeneity in the levels of the variables (i.e. fixed effects). Second, thanks to a
reduced form VAR approach, our results do not rely on assumptions that are nec-
essary in models that use the q-theory of investment or Euler equations. Third, by
analyzing orthogonalized impulse-response functions we are able to separate the re-
sponse of investment to shocks coming form fundamental or financial factors. Finally,
we contribute to the growth literature by presenting new evidence that investment
4
in firms operating in financially underdeveloped countries exhibits dynamic patterns
consistent with the presence of financing constraints. This finding highlights the role
of financial development in improving capital allocation and growth.
Our paper is closely related to several recent papers. Gilchrist and Himmelberg
(1995 and 1998) were the first to analyze the relationship between investment, future
capital productivity and firms' cash flow with a panel-data VAR approach. They use
a two-stage estimation procedure to obtain measures of what they call 'fundamen-
tal' q and 'financial' q. These factors are then substituted in a structural model of
investment, which is a transformation of the Euler equation model. Unlike Gilchrist
and Himmelberg, we do not estimate a structural model of investment, but instead
study the unrestricted reduced-form dynamics afforded by the VAR (which is in ef-
fect the first stage in their estimation). Stanca and Gallegati (1999) also investigate
the relationship between firms' balance sheets and investment by estimating reduced
form VARs on company panel data for UK firms. Despite some differences in the
specification of the empirical model and the estimation methodology, the approach
and the results of their paper are similar to ours. However, they do not present an
analysis of the impulse-response functions which we consider the main tool in sepa-
rating the role of financial variables in companies' investment decisions. In addition,
the distinguishing feature of our paper is the focus on the differences in the dynamic
behavior of firms in countries with different levels of financial development.
Our paper is also related to Love (2002) who uses the Euler-equation approach
and shows that financing constraints are more severe in countries with lower levels of
5
financial development, the same as we find in this paper. However, the interpretation
of the results in the previous paper is heavily dependent on the assumptions and
parameterization of the model, while the approach we use here imposes the bare
minimum of restrictions on parameters and temporal correlations among variables.
The rest of the paper is as follows: Section 2 presents the empirical methodology,
Section 3 presents the data description; Section 4 provides the results and Section 5.
presents our conclusions.
2 Empirical methodology
Our approach is to use a panel data Vector Autoregression (VAR) methodology. This
technique combines the traditional VAR approach, which treats all the variables in
the system as endogenous, with panel-data approach, which allows for unobserved
individual heterogeneity. We present a discussion of the,standard VAR model and
the impulse-response functions in Appendix 1.
We specify a first-order three-variable VAR model as follows:
z-.t = ro + rlzit-l + fi + d.(t + et1)
where Zt is one of the two tree-variable vectors: {sk, ik, cf k} or {sk, ik, cak}; sk is a
sales to capital ratio and it is our proxy for the marginal productivity of the capital,3
3See Gilchrist, and Himmelberg (1998) for a derivation of the ratio of sales to capital as a measure
of marginal productivity of capital.
6
ik is the investment to capital ratio which is our main variable of interest. We use
two proxies for 'financial' factors: one is cfk which is cash flow scaled by capital,
and the other one is cak, a ratio of cash stock to capital. Although cash flow is the
most commonly used proxy for net worth it is closely related to operating profits and
therefore also to marginal product of capital. If the investment expenditure does not
result in higher sales but in lower costs (i.e. more efficiency), the sales to capital ratio
would not pick up this effect, while the cash flow measure would. Thus, even in a
VAR framework there is still a chance that cash flow would pick up a portion of the
fundamental factor rather than financial factor. Therefore we prefer to use cash stock
as our main proxy for 'financial' factors.
Since cash stock is a 'stock' rather than a 'flow' variable, it is much less likely to
be correlated with fundamental factors than is cash flow. In addition, cash stock has
an intuitive interpretation as "cash on hand" that firms can use for investment if the
opportunities arrive. One theoretical justification for the cash stock measure appears
in the Myers and Majluf (1984) model, where the amount of cash holdings, which
the authors call "financial slack," has a direct effect on investment in the presence of
asymmetric information. This slack allows firms to undertake positive NPV projects,
which they would pass up if they did not have any internal funds. This implies that
if external financing is costly, there will be a positive relationship between investment
and cash stock.
We focus our analysis on the impulse-response functions, which describe the reac-
tion of one variable in the system to the innovations in another variable in the system,
7
while holding all other shocks at zero. However, since the actual variance-covariance
matrix of the errors is unlikely to be diagonal, to isolate shocks to one of the VAR
errors it is necessary to decompose the residuals in a such a way that they become
orthogonal. The usual convention is to adopt a particular ordering and allocate any
correlation between the residuals of any two elements to the variable that comes first
in the ordering.4 The identifying assumption is that the variables that come earlier in
the ordering affect the following variables contemporaneously, as well as with a lag,
while the variables that come later only affect the previous variables with a lag. In
other words, the variables that appear earlier in the system are more exogenous and
the ones that appear later are more endogenous.
In our specification we assume that current shocks to the marginal productivity
of capital (proxied by sales to capital) have an effect on the contemporaneous value
of investment, while investment has an effect on the marginal productivity of capital
only with a lag. We believe this assumption is reasonable for two reasons. First, the
sales is likely to be the most exogenous firm-level variable available since it depends
on the demand for the firm's output, which often is outside of the firms' control (of
course, sales depend on the firm's actions as well but most likely with a lag). Second,
investment is likely to become effective with some delay since it requires time to
become fully operational (so called a "time-to-build" effect). We also argue that the
effect of sales on either cash flow or cash stock is likely to be contemporaneous and
4The procedure is know as Choleski decomposition of variance-covariance matrix of residuals
and is equivalent to transforming the system in a "recursive" VAR for identification purposes. See
Appendix 1 for the derivations and further discussion of impulse-responce functions.
8
if there is any feedback effect it is likely with a lag. Finally, we assume that cash
stock responds to investment contemporaneously, while investment responds to cash
stock with a lag. This is because the firm will consider last year's stock of cash while
making this year's investment decision, while the end of year cash stock will definitely
reflect the current year investment.5
Our analysis is implicitly based on an investment model in which, after controlling
for the marginal profitability, the effect of the financial variables on investment is
interpreted as evidence of financing constraints.6 We do this informally, by relying on
the orthogonalization of impulse-responses. Because the shocks are orthogonalized, in
other words the 'fundamentals' are kept constant, the impulse response of investment
to cash stock isolates the effect of the 'financial' factors.
Our main interest is to compare the response of investment to financial factors in
countries on a different level of financial development. To do that we split our firms
into two samples according to the level of financial development of the country in
which they operate and study the difference in impulse-responses for the two samples.
We refer to these two groups as 'high' (financial development) and 'low' (financial
development), but this distinction is relative and is based on the median level of
financial development among countries in our sample.7
In applying the VAR procedure to panel data, we need to impose the restriction
5We present the resutls of the model that includes cash flow in the same order for comparison
purposes, however these results are robust to changing the order of cash flow and investment.
6See Gilchrist and Himmelberg (1998) for a more formal structural model that is behind their
first-stage reduced VAR approach, which is similar to our approach.
7A recent paper by Powell et al. (2002) uses similar approach to ours (i.e. splitting the countries
into two groups and estimating VARs separately for each group) to study the interrelationships
between inflows and outflows of capital and other macro variables.
9
that the underlying structure is the same for each cross-sectional unit. Since this
constraint is likely to be violated in practice, one way to overcome the restriction
on parameters is to allow for "individual heterogeneity" in the levels of the variables
by introducing fixed effects, denoted by fi in the model. Since the fixed effects
are correlated with the regressors due to lags of the dependent variables, the mean-
differencing procedure commonly used to eliminate fixed effects will create biased
coefficients. To avoid this problem we use forward mean-differencing, also referred
to as the Helmert procedure (see Arellano and Bover 1995). This procedure removes
only the forward mean, i.e. the mean of all the future observations available for each
firm-year. Since this transformation preserves the orthogonality between transformed
variables and lagged regressors, we use lagged regressors as instruments and estimate
the coefficients by system GMM.8
Our model also allows for country-specific time dummies, d,,t, which are added
to the model (1) to capture aggregate, country-specific macro shocks that may affect
all firms in the same way. We eliminate these dummies by subtracting the means of
each variable calculated for each country-year.
To analyze the impulse-response functions we need some estimate of their confi-
dence intervals. Since the matrix of impulse-response functions is constructed from
the estimated VAR coefficients, their standard errors need to be taken into account.
Since analytical standard errors are computationally difficult to implement, we report
standard errors of the impulse response functions by using Monte Carlo simulation to
8In our case the model is "just identified," i.e. the number of regressors equals the number of
instruments, therefore system GMM is numerically equivalent to equation-by-equation 2SLS.
10
generate their confidence intervals.9 To compare the impulse-responses across our two
samples (i.e. 'high' and 'low' financial development) we simply take their difference.
Because our two samples are independent, the impulse-responses of the differences
are equal to the difference in impulse-responses (the same applies to the simulated
confidence intervals).
3 Data
Our firm-level data comes from the Worldscope database, which contains stardardized
accounting information on large publicly traded firms and it contains 36 countries
with over. 7000 firms for the years 1988-1998. Table 1 gives the list of countries
in the sample with the number of firms and observations per country, while details
on the sample selection are given in Appendix 2. The number of firms included in
the sample varies widely across the countries and the less developed countries are
underrepresented. The US and UK have more than 1000 firms per country, while
the rest of the countries have only 136 firms on average (Japan is the third largest
with over 600 firms). Such a prevalence of US and UK companies will overweight
these countries in the cross-country regressions and prevent smaller countries from
influencing the coefficients. To correct for this we use only the largest firms within
91n practice, we randomly generate a draw of coefficients r of model (1) using the estimated
coefficients and their variance-covariance matrix and re-calculate the impulse-resonses. We repeat
this procedure 1000 times (we experimented with a larger number of repetitions and obtained similar
results). We generate 5th and 95th percentiles of this distribution which we use as a confidence
interval for each element of impulse-response. Stata programs used to estimate the model and
generate impulse-response functions and their confidence intervals are available from the authors.
each country. The inclusion criteria are based on firm ranking, where rank 1 is given
to the largest firm in each country. We limit our analysis to the largest firms in each
countries because we want to compare firms of the same "type" across countries (i.e.
large firms with large firms) to isolate any size effect.
We construct the index of financial development, FD by combining standardized
measures of five indicators from Demirguc-Kunt and Levine (1996): market capi-
talization over GDP, total value traded over GDP, total value traded over market
capitalization, the ratio of liquid liabilities (M3) to GDP and the credit going to the
private sector over GDP. We split the countries into two groups based on the median
of this indicator. We refer to these two groups as 'high' (financial development) and
'low' (financial development), but we remind the reader that this distinction is rel-
ative and is based on the median level of financial development among countries in
our sample.
Table 2 summarises all the variables used in the paper (note that we normalize all
the firm-level variables by the beginning-of-period capital stock), and Table 3 reports
the distribution of cross-country firm level variables.
4 Results
The main results are reported in Tables 4 and 5. We report the estimates of the
coefficients of the system given in (1) where the fixed effects and the country-time
dummy variables have been removed. In Table 4 we report the results of the model
with cash stock, while in Table 5 we report the model with cash flow. We report the
12
results that include only up to 150 largest firms in each country using a rank-based
approach described in the data section.10 We present graphs of the impulse-response
functions and the 5% error bands generated by Monte Carlo simulation. Figure
1 reports graphs of impulse-responses for the model with cash stock estimated for a
sample of countries with 'low' financial development, while Figure 2 reports this model
for countries with 'high' financial development. In Figure 3 we show the differences
in impulse-responses of two samples for a model with cash stock (the difference is
'low' minus 'high'). To save space we do not present graphs for the model with cash
flow separately for each sample but only report the differences in impulse-responses
in Figure 4.
We discuss general results first before moving on to the results of our particular
interest. We observe that the response of sales to capital ratio to investment is
negative in the estimated coefficeints and impulse-responses. This is expected as
sales to capital is our proxy for marginal product of capital. A shock to investment
increases the capital stock, which moves the firm along the production frontier. With
diminishing returns to capital, the marginal product will decrease.
The investment shows an expected positive response to a shock in sales to cap-
ital ratio (i.e. marginal profitability), both in the estimated coefficients and in the
impulse-responses (but in the later the positive response is only with a one-year lag
10We have repeated our analysis with other models where we have considered different proxies
for both cash flow and cash stock, and different normalizations (for example, scaling by total assets
instead of capital stock). The results are similar to the ones reported and are available on request.
We also used different cutoff points - such as 50 or 100 firms and obtained similar results (available
on request).
13
because of the negative contemporaneous correlation)."1 Cash stock is increasing in
response to sales shock (higher revenues allow more cash to be kept in cash stock),
while it is decreasing in response to investment (as investment is a major use of cash,
larger invesment implies that there will be less cash left at the end of the year). Cash
stock has no significant effect on sales to capital (and there is no reason to expect such
an effect). All the patterns that we observe are very similar across our two groups of
countries.
The result of particular interest is the response of investment to financial variables-
the cash stock or cash flow. We first observe that the impact of the lagged cash stock
(as well as cash flow) on the level of investment is much larger in countries qith 'low'
financial development than it is in countries with 'high' levels. This difference is most
pronounced in the model with cash stock in which the coefficients are almost three
times larger in the 'low' sample (i.e. 0.036 compared with 0.013 - see last column in
Table 4), and this difference is statistically significant. This is the first evidence that
financial factors have a different effect on investment in countries with different levels
of financial development.
The panels representing the impulse-response of investment, ik, to a one standard
deviation shock in cash stock, cak, clearly show a positive impact. We also notice
that this response has a larger impact on the value of the investment for firms in
'lIn the results reported we scaled all the variables by current period capital stock. This leads to
the contemporaneous negative response of investment to sales to capital, which is purely mechanical
and driven by the scaling factor. This response is positive when we scale all our results by the end of
the previous period capital stock. All our results hold when we scale by end of the previous period
capital stock.
14
'low' sample. This can be seen most clearly in Figure 3 that reports the difference in
two samples responses (i.e. 'low' minus 'high'). The difference between two impulse-
responses is significant at better than 5% (i.e. the 5% lower band is quite above the
zero line). The same is true when we use a model with cash flow instead of cash stock
(Figure 4), however the difference is a little less pronounced.
The orthogonalization of the VAR residuals (discussed in section 2) allows us to
isolate the response of investment to 'financial' factors (cash stock or cash flows)
from the response to 'fundamental' factors (marginal productivity of capital). We
can therefore interpret our results as evidence that the response of investment to
'financial' factors and therefore the intensity of financing constraints is significantly
larger in countries with less developed financial markets.
In conclusion, both the coefficient estimates resulting from the Vector Autoregres-
sions and the impulse-response functions support our claim that in the presence of
financing constraints, which are clearly more stringent in countries that don't have a
well developed financial system, the availability of liquid assets affects firms' invest-
ment decisions. This implies that financial under-development adversely affects the
dynamic investment behavior which leads to inefficient allocation of capital.
5 Conclusions
This paper uses a VAR approach to the analysis of firm-level data and shows that the
availability of internal liquid funds matters more when firms make investment deci-
sions in countries where the financial system is not well developed. More specifically,
15
we find that the impact of a positive shock to cash stock or cash flow is significantly
higher for firms in countries with lower level of financial development. Since the in-
vestment level of firms that are more constrained in their ability to obtain external
financing is affected by shocks to internal funds, the accumulation of capital will be
less efficient in countries that are less financially developed, thus leading to slower
economic growth.
We believe our paper contributes to the literature on financial constraints and
investment decisions as well as to the finance and growth literature. Thanks to a re-
duced form VAR approach, we do not need the strong assumptions that are necessary
in models that use the q-theory of investment or the Euler-equation approach. More-
over, by analyzing impulse-response functions we are able to separate the fundamental
from the financial factors that influence the level of investment, overcoming the prob-
lems stemming from the potential correlation between the proxy for net worth and
the investment opportunities. Our findings highlight the role of financial development
in improving capital allocation and growth.
16
Appendix 1. VAR with Panel Data
A VAR is a multivariate simultaneous equation system, in which each variable
under study is regressed on a finite number of lags of all variables jointly considered.
The VAR approach is useful when the intention is to analyze a phenomenon without
having any strong priors about competing explanations of it. The method focus
on deriving a good statistical representation of the interactions between variables,
letting the data determine the model. In a simple two-variable case, a first-order
vector autoregression model can be written as follows:
xt= alo - a2yt + I311Xt1 + ±312Yt-I + ext (2)
yt = a2- a2lXt + /321Xt1 + 322Yt-1 + EYt (3)
The time path of {xt} is affected by current and past values of the sequence {Yt}
and the time path of {Ye} is affected by current and past realizations of the sequence
{Xt} . The errors e,t and ert are uncorrelated white-noise disturbances with constant
variances. We can rewrite this system as:
a12 Xt alo + 1[ 0 I12 Xt-i + x [ 42,
a2l 1 Yt a2O [21 P22 Yt-il Eyt
or in a more compact form:
Az-t = Ao + Alzt-, +et (5)
17
The model represented by equations (2) and (3) is called a "structural" VAR under
presumption that there exists some underlying theory that provides restrictions on
the matrix A and allows to identify the coefficients. In fact, these equations cannot
be estimated directly due to the correlation of xt with evt and of Yt with et. If we
premultiply the system in (5) by A', we obtain the so-called standard "reduced"
form:
zt = ro + rlzt_l + et (6)
where, rO = A-lAo rli =A-.A1 and et = A-le,. In the.standard form of the
model, the errors et are composites of the white-noise processes et and therefore have
zero means, constant variances, and are .individually serially uncorrelated. However,
the covariance of the elt and e2t.shocks-are not in general equal to zero. The VAR
model in standard form does not present the estimation; problems of the structural
form. The OLS method gives unbiased estimates of the. elements of the matrices ro
and rl, and of the variance-covariance matrix of the errors {et} However, the esti-
mation of the standard model yields fewer estimates than the number of parameters
of the primitive model. Therefore, to identify the system some restrictions on the
parameters of the structural model are necessary (for example, we might impose that
one of the parameters be equal to zero).
The impulse response functions are based 6n the moving average representation
18
of the system, which is the following:
00
Zt = IA +E r;et-i (7)
i=O
where IA is a function of the parameters of the model and rI, is the ith power of the
matrix rI from equation (6). However, this representation would not be very useful
to study the effect of changes in, say, eyt on either {xt} or {yt} because the errors are
correlated and therefore tend to move together. Since the errors {et-i} are a function
of the original shocks {e_} and {e,t}, we can rewrite zt as:
00
Zt = z + E ¢>ict-i (8)
i=O
The coefficients Xi are the impulse-response functions. In a two-variable case,
Ozt/Oct-, = 4S is a matrix where, for example, the element O.',l represents the impact
of a unit shock in ey,t-. on xt. To quantify the cumulative response of an element of
zt to an unpredicted innovation in some component of et, the components of et must
be orthogonal. If we assume that the Q = E (etet) is positive definite, then there
exists a unique lower triangular matrix K with ones along the principal diagonal and
a unique diagonal matrix D with positive entries along the principal diagonal, such
that:
Q = KDK' (9)
19
Let
ut = K-let. (10)
Then E (utut) = K-'Q (K-1)' = D. Since et = Kut, the vector {Zt} has a moving
average representation in terms of ut:
00
zt = # + E KOiut-i (11)
i=O
For example in two-variable case, we will have that
9yt = X8K2, (12)
Ou.,t-.
where Kz is the first column of the matrix K. The plot of (12) as a function of s > 0
is an orthogonalized impulse response function.
20
Appendix 2. Sample Selection
All countries in the Worldscope database (May 1999 Global Researcher CD) with
at least 30 firms and at least 100 firm-year observations are included in the sample
(in addition we include Venezuela (VE), though it has only 80 observations); former
socialist economies are excluded. This results in a sample of 40 countries. The sample
does not include firms for which the primary industry is either financial (one digit
SIC code of 6) or service (one digit SIC codes of 7 and above).
In addition we delete the following (see Table 2 for variable definitions):
- All firms with 3 or less years of coverage;
- All firm-years with missing CAPEX, Sales, Netpeq, Compnumb or Cash;
- Observations with negative Cash (2 obs), Stminv (1 ob), SK (2 obs) or Depre
(26 obs);
- Observations with DAK > 0.7 (2018 obs);
- Outliers for the distributions of SK, IK, CAK and CFK
The resulting dataset has about 54,000 observations. The number of observations
by country is given in Table 1.
21
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Table 1. Sample Coverage Across Countries
Countries are split into two groups based on the median level of financial development.
Number of Percent of
Country Number of Percent of total Number observations, total if Financial
Country code observations observations offirms if rank