We apply the accelerator principle to measure the functional efficiency of capital markets. We estimate the elasticity of capital with respect to output using a panel of firms across 44 countries, and compare the results with existing approaches. Furthermore, we correlate our measure with corporate governance institutions.Allocation of capital; accelerator principle; functional efficiency:

Desai, Sameeksha

Eklund, Johan E.

English

Research Papers in Economics

  1 
A Methodological Note on Measuring the Functional Efficiency of Capital Markets 
 
 
Johan E. Eklund  
Jönköping International Business School 
P.O. Box 1026, 551 11, Jönköping, Sweden 
and The Royal Institute of Technology 
Email: johan.eklund@ihh.hj.se 
 
Sameeksha Desai 
Max Planck Institute of Economics 
10 Kahlaischestrasse, Jena, 07745, Germany 
Email: desai@econ.mpg.de 
 
 
 
 
 
 
 
Abstract  
We  apply  the  accelerator  principle  to  measure  the  functional  efficiency  of  capital 
markets. We estimate the elasticity of capital with respect to output using a panel of firms 
across 44 countries, and compare the results with existing approaches. Furthermore, we 
correlate our measure with corporate governance institutions.  
 
 
JEL classifications: C00, G32, P00 
 
Keywords: Allocation of capital, accelerator principle, functional efficiency 
 
Acknowledgments:  Johan  Eklund  thanks  Sparbankernas  Forskningsstiftelse  and  the 
Söderbergska Foundation; Sameeksha Desai thanks the Kauffman Foundation and Max 
Planck Institute. We thank Zoltan Acs, Åke E. Andersson, David Audretsch, Per-Olof 
Bjuggren,  Börje  Johansson,  Dan  Johansson,  Prashanth  Mahagaonkar,  Roger  Stough, 
Daniel  Wiberg  and  participants  at  seminars  held  at  Jönköping  International  Business 
School. This paper is also available as a working paper at the Max Planck Institute of 
Economics and at the Royal Institute of Technology.  
 
 
 
 
   2 
 
Introduction  
 
The allocation of capital and relevant institutions are critical determinants of economic 
performance, but cross-country research is complicated by the significance of economic 
development. We derive a method where this is not the case. 
 
Econometric Model  
 
To  estimate  the  functional  efficiency  of  capital  allocation
1,  Wurgler  (2000)  estimates 
industry  elasticity  of  investments  with  respect  to  industry  value-added.  Mueller  and 
Reardon  (1993)  do  this  by  estimating  Marginal  q,  which  measures  the  return  on 
investments relative to opportunity cost (see Gugler et al., 2004). The use of Marginal q 
is consistent with conventional investment theory, but Wurgler’s measure is not
2. 
 
To measure capital allocation at the firm level, we modify Wurgler (2000) to make the 
method consistent with the accelerator principle and investment theory. To do this, we 
measure  elasticity  of  capital  with  respect  to  output,  measured  as  sales.  Assuming 
constant  prices,  changes  in  sales  will  be  proportional  to  changes  in  output.  Ceteris 
paribus,  higher  elasticity  of  capital  with  respect  to  sales  means  quicker  response  to 
changes in expected returns and therefore, more efficient capital allocation.  
 
                                                 
1 Tobin (1984). 
2 Wurgler (2000) estimates elasticity of investments with respect to value added, η ,  
as: ε η α +  


 


+ =  


 


− − 1 1
ln ln
t
t
t
t
V
V
I
I
, where I is industry investments (gross fixed capital formulation) and V 
is value added. Presumably he does this for empirical reasons, since he uses aggregated industry data.  
However, one may still expect a high correlation between η  and λ
*.  For elasticity of capital to equal 
elasticity of investments, it is necessary that t t I K ∆ = ∆
∗ . This happens only if  1 1 − − = t t K I δ which implies 
that 1 1 −
∗
− = t t K K . Mueller and Reardon (1993) estimate qm as: ε δ + + − =
−
− −
−
1 1
1
t
t
m
t
t t
M
I
q
M
M M
, where Mt 
and It is market value and investments respectively.    3 
The accelerator model of investments captures time structure and responses to changes in 
expectations. Several proxies can be used as accelerators
3. We choose sales because of 
inconsistent measurements of value-added across industries and countries
4.  
 
In accelerator models, the desired level of capital,
∗
t K  is determined by output, Yt: 
 
t t kY K =
*                   (1) 
 
where k is the capital coefficient (capital-output ratio)
5. We assume 
∗
t K  to equal to actual 
capital, Kt. This means net investments, It and (Kt - Kt-1), are proportional to changes in 
desired stock of capital, 
∗
−
∗ − 1 t t K K . Net investments, NIt, is expressed:  
 
) ( 1 − − = t t t Y Y NI λ                 (2) 
 
Net  investments  are  proportional  to  an  accelerator  λ.  If  t t K K =
∗   then  λ  =  k.  This 
equilibrium  assumption  is  typically  unfulfilled,  but  not  relevant  here
6.  For  gross 
investments,  we  add  replacement  investments  which  are  proportional  to  old  capital, 
1 − t K δ :  
 
t t t Y K I ∆ + = − λ δ 1                 (3) 
 
We divide both sides with Kt-1: 
 
1 1 − −
∆
+ =
t
t
t
t
K
Y
K
I
λ δ                   (4) 
                                                 
3 Tinbergen (1938, 1939), Jorgenson and Siebert (1968), Kuh (1963) and Jorgenson (1971). 
4 Value-added is calculated in two ways: 1) Sales – costs for intermediary goods, 2) Profit + cost of labor. 
Sales are relatively unproblematic but costs of intermediary goods and labor are counted differently across 
countries.  
5 Kaldor (1963) argues this ratio is stable over time.       
6 If fulfilled, there would be efficient allocation all the time, with an elasticity of one. See Jorgenson (1971) 
and Tinbergen (1938).   4 
 
Since  t t kY K =
∗  this is reformulated as:  
 
1 1 −
∗
−
∆
+ =
t
t
t
t
Y
Y
K
I
λ δ                 (5) 
 
where λ
* = (λ/k), which is elasticity of capital with respect to output (sales). This is 
additionally useful because it achieves a normalization that reduces heteroskedasticity, 
making equation 4 possible to estimate. Note that if  t t K K =
∗ at every point in time, then λ 
= k, which means λ
* = 1.  
 
We estimate for each country: 
 
t i
t i
t i
t i
t i
t i
S
S
K
I
,
1 ,
,
1 ,
, ε λ θ α δ +
∆
+ + + =
−
∗
−
            (6) 
 
where 
∗ λ  is elasticity of investments with respect to sales, I is investments made by firm i 
in period t, K is capital stock in period t-1 and S is sales in period t. 
 
Cross-country  panel  studies  are  interested  in  country-specific  estimations  of  capital 
elasticity, favoring a fixed effects model with firm and time effects (αi and θt). 
 
Data 
 
We  use  firm-level  accounting  data  from  Standard  &  Poor’s  Compustat  Global  to 
measure gross investments: 
 
I = After tax profit – dividends + depreciation + ∆Equity + ∆Debt + R&D   
   5 
This adequately reflects actual investments. Using gross investments is more appropriate 
than net investments because it is not possible to obtain reliable estimates for replacement 
investments.  Although  advertising  and  marketing  should  arguably  be  included  in 
investments (Mueller and Reardon, 1993), we exclude them because of inconsistently 
available across countries. Financial firms are excluded from the sample. 
 
The  measure  of  capital  is  selected  to  be  consistent  across  countries.  Variables  are 
adjusted to 2000 constant prices with inflation data from International Financial Statistics 
(IMF). A total of 11984 included firms yield 61292 observations across 44 countries. To 
minimize the weight of outliers, observations for each country are cut five percent at each 
end of the distribution. In Table 1, we group countries by legal origin (see La Porta et al., 
2003).   
 
We  use  the  following  explanatory  variables:  Property  rights  (Holmes  et  al,  1997); 
Minority shareholder protection (Pagano and Volpin, 2005
7); Law and order (averaged 
for 1982-1995, from International Country Risk Guide); Ownership concentration (La 
Porta  et  al,  1998);  Family  ownership  concentration  (La  Porta  et  al,  1999
8).  We  add 
dummies for legal origins (La Porta et al., 2003) classified as English, German, French, 
Scandinavian  and  Socialist/Communist.  We  use  standard  controls  for  economic 
development as logarithm of 1995 GDP and economic growth as average GDP growth 
between 1980 and 2002
9. 
 
Results 
 
We compare our measure with estimates of marginal q by Gugler et al (2004) and find no 
significant correlation. However, marginal q is significantly correlated with ownership 
concentration,  property  rights  and  shareholder  protection.  The  merit  of  our  model  is 
reflected in Table 2. When we regress Wurgler’s elasticity estimates on our measure of 
elasticity, the coefficient is close to one (Table 3). The interesting comparison between 
                                                 
7 This is an extended version of La Porta et al (1998), also called the LLSV Pagano-Volpin anti-director 
index. It covers 1993 to 2001; we use the average. 
8 This is measured as control rights, not cash-flow rights. Data for Indonesia, Philippines, Taiwan and 
Thailand is from Claessens et al (2000). 
9 Data for both is from World Development Indicators; data for Taiwan is from La Porta et al. (1997).   6 
Wurgler (2000) and our measure is the correlation with control variables. GDP growth is 
significant and negatively correlated with both our measure (-0.34) and Wurgler (-0.4). 
However, current GDP is positively and significantly correlated with Wurgler’s measure 
(0.44)  but  not  our  measure.  This  suggests  our  measure  is  not  sensitive  to  economic 
development but is sensitive to economic growth. This makes it robust for cross-country 
study. 
 
Results for legal origin do not support the legal origins hypothesis (La Porta et al., 1998). 
We  find  weak  protection  of  property  combined  with  high  ownership  concentration, 
particularly family, appear to hamper capital allocation. Property rights and law and order 
have a positive and significant correlation (at the 5% level) with elasticity. 
 
There are several explanations for capital elasticity greater than one. First, indivisibilities 
of production factors may make the production function discontinuous, so output cannot 
be  produced  proportionally  to  capital.  Second,  “excessive  expectations”  may  affect 
estimates (Manne, 1945). Third, if It or Kt contain measurement errors, this can create 
scaling  effects  so  estimated  elasticity  deviates  from  its  true  value.  However,  this  is 
unlikely to be problematic here since variables were chosen for consistent cross-country 
estimation. This is why we use sales to measure output. Any measurement error will be 
consistent  across  all  countries,  since  elasticity  is  a  relative  measure  of  efficiency  of 
capital allocation. An interesting next step is to compare firms within a country. 
 
 
 
 
 
 
 
 
 
 
 
 
 
   7 
References 
 
Claessens, S., Djankov, S. and Lang, L.H.P, 2000, The Separation of Ownership and 
Control in East Asian Corporations, Journal of Financial Economics 58, 81-112.  
Gugler, K, Mueller, D. and Yurtoglu, B, 2004, Corporate Governance and the Return on 
Investments, Journal of Law and Economics 47, 589-633.  
Holmes, K., Johnson, B. and Kirkpatrick, M, 1997, 1997 Index of Economic Freedom 
(The Heritage Foundation, Washington D.C.). 
Jorgenson, D, 1971, Econometric Studies of Investment Behavior: A Survey, Journal of 
Economic Literature 9, 111-1147. 
Jorgenson, D and Siebert, C, 1968, A Comparison of Alternative Theories of Corporate 
Investment Behavior, American Economic Review 58, 681-712. 
Kaldor, N, 1963, Capital Accumulation and Economic Growth, in: Lutz, F. and Hague, 
D, eds, The Theory of Capital (MacMillan, London) 177-222. 
Kuh, E, 1963, Theory and Institutions in the Study of Investment Behavior, American 
Economic Review 53, 260-268.  
La  Porta,  R.,  Lopez-de-Silanes,  F.,  Pop-Eleches,  C.,  and  Shleifer,  A,  2003,  Judicial 
Checks and Balances, NBER working paper no. 9775.   
La Porta, R., Lopez-De-Silanes, F., Schleifer, A. and Vishny, R, 1998, Law and Finance, 
Journal of Political Economy 106, 1113-1155. 
---1997, Legal Determinants of External Finance, Journal of Finance 52, 1131-1150. 
Manne, A.S, 1945, Some Notes on the Acceleration Principle, Review of Economics and 
Statistics 27, 93-99.   
Mueller, D. and Reardon, E, 1993, Rates of Return on Corporate Investment, Southern 
Economic Journal 60, 430-453.   
Pagano,  M  and  Volpin,  P,  2005,  The  Political  Economy  of  Corporate  Governance, 
American Economic Review 95, 1005-1030.   
Tinbergen, J, 1939, “A Method and its Application to Investment Activity” in: Statistical 
Testing of Business Cycle Theories, vol. 1 (League of Nations, Geneva).  
---1938, Statistical Evidence on the Acceleration Principle, Economica 5, 164-176.   
Tobin, J, 1984, On the Efficiency of Financial System, Lloyd’s Banking Review 1, 1-15.  
Wurgler, J, 2000, Financial Markets and the Allocation of Capital, Journal of Financial 
Economics 58, 187-214.  
 
 
 
 
 
 
 
 
 
 
 
 
   8 
Table 1   Capital elasticities with respect to Sales, 
∗
j λ ˆ  
Country  ∗
j λ ˆ   t-value  Std. Err.  R
2  No. firms  No. obs.  Period 
 
Australia 
 
0.621 
 
13.7 
 
0.045 
 
0.09 
 
377 
 
2047 
 
1999-2005 
Canada  0.849  15.0  0.057  0.14  303  1646  1999-2005 
Hong Kong  0.756  8.24  0.092  0.12  101  550  1999-2005 
India  0.687  13.6  0.051  0.17  169  912  1999-2005 
Ireland  1.464  6.99  0.210  0.26  33  178  1999-2005 
Israel  0.609  2.05  0.297  0.06  26  140  1999-2005 
Malaysia  0.400  16.4  0.024  0.15  524  2371  1999-2005 
New Zealand  0.829  3.02  0.275  0.07  52  234  2000-2005 
Pakistan  0.367  3.09  0.119  0.12  26  164  1998-2005 
Singapore  0.776  18.9  0.041  0.25  301  1363  2000-2005 
South Africa  1.064  6.26  0.170  0.09  114  512  2000-2005 
Thailand   0.523  9.91  0.053  0.13  217  1182  1999-2005 
United Kingdom  1.276  18.8  0.068  0.09  691  3774  1999-2005 
United States  1.160  42.5  0.027  0.16  2137  11642  1999-2005 
English legal  origin average
a 
 
0.884 
(0.813) 
 
54.7  0.016  0.11  5071  26715  - 
Argentina  0.600  7.73  0.078  0.37  21  114  1999-2005 
Belgium  1.266  8.05  0.157  0.18  72  400  1999-2005 
Brazil   0.551  8.41  0.066  0.15  96  524  1999-2005 
Chile  0.431  7.96  0.054  0.20  80  438  1999-2005 
Colombia  0.283  1.88  0.151  0.13  10  54  1999-2005 
France  1.575  14.8  0.106  0.10  362  1976  1999-2005 
Greece  1.034  9.96  0.104  0.27  55  296  1999-2005 
Indonesia  0.342  4.92  0.069  0.07  170  764  1999-2005 
Italy  0.937  8.14  0.115  0.11  160  738  2000-2005 
Mexico  0.715  8.58  0.083  0.31  57  308  1999-2005 
The Netherlands  1.595  11.2  0.142  0.15  113  620  1999-2005 
Peru  0.675  8.89  0.075  0.44  18  123  1997-2005 
The Philippines  0.645  12.8  0.050  0.31  69  373  1999-2005 
Portugal  1.219  6.62  0.184  0.30  26  140  1999-2005 
Spain  0.942  11.8  0.080  0.25  76  410  1999-2005 
Turkey  0.567  2.53  0.224  0.06  29  156  1999-2005 
French legal origin average
a 
 
1.155 
(0.836) 
 
27.6  0.042  0.10  1414  7434  - 
Austria  1.167  7.47  0.156  0.25  43  248  1999-2005 
Germany  1.579  18.7  0.085  0.12  431  2344  1999-2005 
Japan  0.603  38.5  0.016  0.24  2860  13230  2000-2005 
South Korea   0.817  21.4  0.038  0.35  203  927  2000-2005 
Switzerland  0.946  12.6  0.075  0.21  142  782  1999-2005 
Taiwan  0.725  16.0  0.045  0.26  180  972  1999-2005 
German legal origin average
a 
 
1.098 
(0.973) 
 
48.6  0.023  0.13  3859  18503  - 
Denmark  0.977  7.08  0.138  0.12  86  470  1999-2005 
Finland  1.619  9.21  0.176  0.20  84  454  1999-2005 
Norway  2.340  5.38  0.435  0.07  89  404  2000-2005 
Sweden  1.177  6.91  0.170  0.05  173  961  1999-2005 
Scandinavian legal  origin average
a 
 
1.279 
(1.528) 
 
11.2  0.115  0.06  432  2289  - 
China  0.482  30.5  0.016  0.21  1130  6108  1999-2005 
Hungary  0.730  4.41  0.165  0.29  11  60  1999-2005 
Poland  1.331  5.88  0.227  0.29  19  119  1998-2005 
Russia  0.434  3.42  0.127  0.36  12  64  1999-2005 
Socialist/communist legal  
 origin average
a 
 
0.492 
(0.744) 
 
31.2  0.016  0.20  1172  6351  - 
Average / total
a  0.914 
(0.902) 
 
77.5  0.012  0.10  11948  61292  - 
a These are weighted averages. Note that this gives different weights to countries. Simple averages  ∗
j λ ˆ are in brackets.   9 
Table 2  Correlation Matrix 
  ∗
j λ ˆ   Ownership 
(mean) 
Ownership  
(median) 
Family 
ownership 
(10%) 
Family 
ownership 
(20%) 
Property 
rights 
shareholder 
protection 
Law and 
order 
Log 
GDP 
GDP 
growth 
Marginal q, 
qm  
 
∗
j λ ˆ  
  
  1                     
Ownership (mean)  - 0.27    1                   
Ownership (median)  - 0.32    0.96    1                 
Family ownership (10%)  - 0.48*    0.53*    0.59*    1               
Family ownership (20%)  - 0.49*    0.54*    0.57*    0.95*    1             
Property rights    0.43*  - 0.51*  - 0.55  - 0.60*  - 0.61*    1           
shareholder protection  - 0.20  - 0.21  - 0.20  - 0.30  - 0.29  - 0.10    1         
Law and order    0.61*  - 0.44*  - 0.46*  - 0.54*  - 0.61*    0.74*  - 0.17    1       
Log GDP    0.16  - 0.54*  - 0.54*  - 0.34  - 0.38*    0.19  - 0.02    0.41*    1     
GDP growth  - 0.34*  - 0.26  - 0.22    0.27    0.30    0.17    0.10  - 0.17    0.03    1   
Marginal q, qm     0.12  - 0.40*  - 0.47*  - 0.19  - 0.17    0.44*    0.33*    0.24    0.28    0.28    1 
j η ˆ     0.53*  - 0.32  - 0.34  - 0.38  - 0.50*    0.59*  - 0.03    0.71*    0.44*  - 0.48*  - 0.13 
Note: * indicates significance at 5 percent. j η ˆ is estimated by Wurgler  (2000). Marginal q from Gugler et al. (2004).  
 
   10 
 
 
Table 3    Elasticity  of  capital,  elasticity  of 
investments and marginal q  
Explanatory variables:          Dependent variable: 
∗
j λ ˆ  
 Constant  0.405** 
(2.38) 
 
0.759*** 
(3.88) 
j η ˆ    0.929*** 
(3.49) 
 
- 
qm,j  -  0.192 
(0.78) 
 
R
2  0.28  0.01 
No. observations  34  44 
Note: *, ** and *** indicate significance at 10, 5 and 1 percent respectively. Ordinary Least 
Squares (OLS) is used as estimator.    

A Methodological Note on Measuring the Functional Efficiency of Capital Markets

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