Appendix
Teun Brinkman
Master Thesis - M.Sc Econometrics Final Version
December 31, 2010
Appendix
A Data descriptions
In table A.1, we give our data descriptions, which are not immediately clear from the main text.
All other …rm-speci…c variables are described in full details in the paper, most often in section 4.1. Our …rm-speci…c variables are collected with the help of Prof.Dr. Ichiro Tokutsu from Kobe University. The data is from non…nancial publicly traded companies from the Firm-level Data Base of the Development Bank of Japan. All …rm-speci…c variables are de‡ated using the CPI (described below). Stocks (e.g. debt, cash) are de‡ated using the index value in March. Flows (cash ‡ow, sales) are de‡ated using the …scal year (April this year to March next year) average index value.
Table A.1. Data descriptions …rm-speci…c variables.
Variable Description
Cash ‡ow Net income divident cost interest cost+depreciation
Market-to-book ratio Assets at marketvalue=by assets at bookvalue Assets at marketvalue Equity at marketvalue+debt at bookvalue
Equity at market value Shares outstanding exp 12 (log (Plow) + log (Phigh)) , wherePlow is the year lowest share price andPhigh is the year highest share price
Industry i;t Standard deviations of cash ‡ow over this and the four previous years,
averaged over industry (with a minimum of two years to compute).
The CPI de‡ator, real GDP per capita growth and the real Tokyo bank stock index come from the Statistics bureau of the Japanese Ministry of Internal A¤airs and Communications (www.stat.go.jp). GDP per capita growth and the Tokyo bank stock index are de‡ated using the year average CPI de‡ator. Data on the treasury bill rate, and the government bond yield spread are monthly data retreived from the IMF, International Financial Statistics database.
The non…nancial corporate credit spread comes from Bloomburg. The …rm-data on bond and CP ratings is also retreived from Bloomburg.
B Descriptive statistics
In table A.2, we present summary statistics of the main variables used throughout the paper.
The most common reporting month in Japan in March. Throughout the paper we only use data from …rms that use March. This led us to a removal of about a …fth of all …rm-year observations.
In table A.3 we report the pairwise correlation coe¢ cients for the levels and …rst-di¤erences of the main variables used throughout the paper.
Table A.2. Summary Statistics Japanese Corporations from 1991 to 2003.
Table present summary statistics of main variables used in the paper, before winsorization. For the
…rst free cash ‡ow to assets measure, we measure free cash ‡ow as the di¤erence between cash ‡ow and capital expenditures. For the second measure, we take the di¤erence between cash ‡ow and depreciation to assets. For more variables descriptions, see appendix A and table A.1. For cash to sales, there are four missing values, since four …rm-year observations report a zero for sales. The average JPY/USD exchange rate for …scal years 1991 to 2003 was 115.95, using monthly nominal exchange rate data from the IMF International Financial Statistics database.
First Third
Mean St.dev. quartile Median quartile Firm-years
Cash/Assets 0.108 0.091 0.045 0.085 0.147 13565
Cash/Sales 0.145 0.191 0.049 0.093 0.172 13561
log(Cash/Net Assets) -2.485 1.110 -3.060 -2.379 -1.761 13565
Cash ‡ow/Assets 0.0286 0.0604 0.0103 0.0306 0.0514 13565
Free cash ‡ow/Assets1 -0.0005 0.0570 -0.0112 0.0021 0.0176 13565
Free cash ‡ow/Assets2 -0.0370 0.0835 -0.0596 -0.0204 0.0051 13565
Real asset size (2005 bln =Y) 303.0 858.2 40.9 80.8 207.9 13565
Real sales (2005 bln =Y) 275.0 1016.0 33.9 74.5 184.1 13565
Market-to-book ratio 1.478 8.461 0.971 1.169 1.439 13565
Industry 0.0176 0.0088 0.0110 0.0160 0.0218 13565
Total debt/Assets 0.559 0.206 0.420 0.568 0.718 13565
Short-term debt/Assets 0.372 0.179 0.237 0.349 0.480 13565
Long-term debt/Assets 0.187 0.140 0.076 0.163 0.264 13565
Net working capital/Assets 0.066 0.071 0.017 0.045 0.090 13565
Capital exp./Assets 0.055 0.165 -0.052 0.051 0.165 13565
[Insert table A.3.]
In table A.4, we present the correlations between our …ve …nancial constraints criteria.
C Robust Hausman tests for …xed e¤ects
The Hausman test, tests whether the di¤erences between two estimators is systematic. Usually, two estimators can be distinguished in terms of e¢ ciency and consistency. The more e¢ cient estimator is potentially inconsistent, while the more consistent estimator could be less e¢ cient.
For the standard Hausman test, it is assumed that the more e¢ cient estimator is fully e¢ cient but potentially inconsistent. Since one of these estimators is e¢ cient, we can compute the
Table A.4. Pairwise correlations …nancial constraints criteria.
FC#1 FC#2 FC#3 FC#4 FC#5
Constrained …rms / 465 461 477 649 922
…rm-year observations 4,754 4,754 4,945 7,088 10,225
Unconstrained …rms / 397 394 578 553 280
…rm-year observations 4,758 4,755 6,933 6,477 3,340
Correlations with:
-FC#2 0.088
-FC#3 0.561 0.160
-FC#4 0.592 0.085 0.591
-FC#5 0.597 0.131 0.418 0.535
Hausman test statistic by simply subtractring the variance-covariance matrices.
However, when the more e¢ cient estimator is not fully e¢ cient, the estimators are not independent and we cannot subtract the variance-covariance matrices. This is already the case under very mild assumptions, such as heteroskedasticity in error terms. Therefore, to apply the Hausman test ,we need to compute the robust Hausman test as in Cameron and Trivedi (2005), p. 718. This test is based on a bootstrap method.
With bEF F as the column vector of more e¢ cient but potentially inconsistent estimates and bCON as the column vector of less e¢ cient but consistent estimates, the robust Hausman test is computed as
H = bEF F bCON Th VbBooth
bEF F bCONii 1
bEF F bCON 2 dimh bEF Fi
where
VbBooth
bEF F bCONi
= 1
B 1
XB b=1
bb bb bb bb T
and
b = bEF F bCON
In these equations, B is the amount of bootstraps (5,000 in our case). The robust Hausman test is 2distributed with dimh
bEF Fi
degrees of freedom.
For each bootstrap we reshu- e the data (with replacement) and estimate the coe¢ cients on a data set of the same size as the original data set. Doing this, we keep the rows of the explanatory variables matrix and the instrument matrix intact. Fixed e¤ects estimation is done, using the
…rst-di¤erences estimator for …xed e¤ects. Since we do not want to compare two inconsistent results, we always used our most consistent result in the test. For example, to test for the
inclusion of …rm …xed e¤ects, we exclude …rm …xed e¤ects from our most consistent estimator which includes both …rm and year …xed e¤ects. For all equations we include the instrument set as used in the paper. These instruments are lagged values for the lagged dependent variable, long-term debt, capital expenditures and net working capital. Table A.5 shows the results.
Table A.5. Robust Hausman Tests for Firm and Year Fixed E¤ects.
See the main text for a description of these Hausman tests.
H0:Exclusion does not a¤ect results systematically
Excluding year and …rm 413.105
…xed e¤ects (0.000)
Excluding year …xed 26.235
e¤ects (0.001)
Excluding …rm …xed 416.135
e¤ects (0.000)
We see that both year and time …xed e¤ects a¤ect the coe¢ cients systematically, suggesting that consistent estimation requires both year and …rm …xed e¤ects. The inclusion of year …xed e¤ects has a smaller but still signi…cant e¤ect on the coe¢ cients.
D Weak versus strong exogenous regressors
The robust Hausman test can also be used to test whether the …rst-di¤erence estimator for …xed e¤ects or the within estimator for …xed e¤ects is more appropriate. Consistency of the within estimator of …xed e¤ects, requires that the instrumental variables are strongly exogenous with respect to the error term. In the regression yi;t = xTi;t + "i;t, with instrument set zi;t, this implies that
E "i;sjzTi;t = 0 for s 6= t
Consistent estimation with the …rst-di¤erences estimator for …xed e¤ects, requires a less strong assumption: weak exogeneity of the instruments. The assumption can be written as
E "i;sjzTi;t = 0 for s > t
This assumption is also referred to as predeterminedness. The less strong assumptions needed for this estimator also implies that this estimator is less e¢ cient. Doing a robust Hausman test for the di¤erences these two estimators, we …nd a 2-statistic of 194.11, implying that at the 1%
level, we reject that the estimators are systematically equivalent.
E Instrument tests
In this section we present results from three tests for the use of instruments: endogeneity tests, weak instrument tests and overidenti…cation tests. First, we present the results from two types of endogeneity tests: the robust Hausman test and tests based on auxilary regressions (Hausman (1978)). If we use instruments for exogenous regressors, our estimator is ine¢ cient. Second, in- struments need to correlate enough with the endogenous regressors. Therefore we test whether we have any weak instruments. Finally, the instruments might correlate with the dependent vari- able, implying that the instruments are not independent from the dependent variable as required.
Test for potential overidenti…cation, as this is called, are reported in the third subsection.
E.1 Endogeneity tests
We test for endogeneity using two methods. First, we use the robust Hausman test. Next to this, we use auxiliary regressions as in Hausman (1978). This is an alternative to the robust Hausman test, provided that we use heteroskedasticity and autocorrelation-robust standard errors (see Cameron and Trivedi (2005), p.276). The disadvantage of the test using auxilary regression is that we require assumptions about the error structure. The advantage is that it is much faster and easier to compute.
The auxilary regression test is performed as follows. Suppose we have the following stacked regression
y = xTunknown 1+ xTendo 2+ xTexo 3+ u
Where y is the dependent variable, xTend is a matrix of instrumented endogenous regressors, xTexois a matrix of exogenous regressors and xTunknownis potentially endogenous. To test whether the variables in xTunknownare endogenous, we regress these variables on the full instrument set, including the already existent instruments and the exogenous regressors. We store the residuals in a matrix buand add them to the regression above as follows
y = xTunknown 1+ xTendo 2+ xTexo 3+ubT + u (1) When is signi…cantly di¤erent from zero, the regressors in xTunknown are likely to be en- dogenous and we include instruments for this variable. Table A.6 reports the results of six tests.
The table presents the coe¢ cients and t-statistics of the error of the …rst-stage regression. In the second-stage regression we instrument all other variables. Robust Hausman test statistics are reported at the bottom of table A.6.
We see in this table, that all error terms enter the auxilary regressions signi…cantly, even indi- vidually, leading us to assume exogeneity. This is also con…rmed from the robust Hausman test.
Judging from the t-statistics in the …rst column, and the robust Hausman test, the endogeneity of the lagged dependent variable and capital expenditures, is the least obvious.
Table A.6. Auxilary Regression Tests and Robust Hausman Tests for Endogeneity.
Each column reports coe¢ cient estimates and t-statistics between brackets of the baseline regression including residuals from …rst-stage regressions for potentially endogenous variables. t-statistics are reported between brackets, and are based on the cluster-robust estimate of the variance-covariance matrix, which controls for both heteroskedasticity and between-…rm correlation in errors. The …rst- stage regressions are estimated by assuming the same (co)variance structure. */**/*** denote statistical signi…cance at the 10/5/1 level. A statistically signi…cant coe¢ cient implies endogeneity of the regressor to which the residual of the …rst-stage regression belongs. In the lower two rows, robust Hausman test results are reported of the di¤erence between the consistent baseline regression and a regression where some of the regressors are not instrumented. The null hypothesis is no systematic di¤erence in estimates, implying no endogeneity. Column (1) tests whether all endogenous variables together show any signi…cance. Column (2) tests the endogeneity of all endogenous variables except for the lagged dependent variables. Columns (3)-(6) test the endogeneity of individual regressors.
Error from …rst-stage H0:b = 0in (1)
regression for (1) (2) (3) (4) (5) (6)
Cash/Assetsi;t 1 0.328*** 0.216***
(5.003) (2.913)
Long-term debt/ 0.557*** 0.509*** 0.267***
Assetsi;t (6.319) (6.441) (4.777)
Capital expenditures 0.0965*** 0.113*** 0.180***
Assetsi;t (4.852) (7.566) (7.119)
Net working capital -0.410*** -0.366*** -0.154***
Assetsi;t (-6.662) (-6.794) (-5.126)
Robust Hausman test 169.267 34.307 13.5223 16.803 15.568 43.6640
(p-value) (0.000) (0.000) (0.095) (0.032) (0.049) (0.000)
E.2 Weak instrument tests
We test for weak instruments by performing an F-test on the set of instruments in …rst-stage regressions, one for each instrumented variable. For example, the …rst-stage regression for the lagged cash holdings can be written as
CashHoldingsi;t 1 = 1CashHoldingsi;t 2+ 2Long-termDebti;t 1+ 3CapitalExpendituresi;t 1 + 4NetWorkingCapitali;t 1+ 5CashFlowi;t+ 6 Sizei;t+ 7 qi;t
+ 8 Industry i;t+ t+ ui;t
Note that exogenous variables are in …rst-di¤erences, as this is the …rst-stage regression for the …rst-di¤erences IV model. In particular we perform a F-test for the null hypothesis that
1 = 2 = 3 = 4 = 0, with the alternative hypothesis that at least on of these is not 0. In table A.7, we can see that we get in this particular case, an F-test results of 228.25, implying that we reject the null hypothesis. Other results are presented in table A.7.
Table A.7. F-tests for Weak Instruments.
See the main text for a description of these F-tests.
Instruments
Instruments for 1 lag 2 lags, all else 1 lag all 2 lags
Cash/Assetsi;t 1 228.25*** 142.14*** 64.41***
Long-term debt/Assetsi;t 340.60*** 261.23*** 105.05***
Capital exp./Assetsi;t 1043.17*** 1020.70*** 123.70***
Net working cap./Assetsi;t 330.75*** 268.43*** 172.86***
As we use lags as instruments for di¤erenced variables, …nding appropriate instruments did not particularly worry us. In table A.7, we see that we reject for all instruments that they are weak at the 1% level. We also observe, that the full set of instruments is more strong when we use less instruments. This is also one of our two motivations for using one instrument per endogenous variable. The other reason is avoiding overidenti…cation.
E.3 Overidenti…cation tests
If instrumental variables are not really exogenous with respect to the dependent variable, this could lead to overidenti…cation. Overidenti…cation results in inconsistent estimation. We im- plement this test as follows. Testing for overidenti…cation (or instrument exogeneity) for just- identi…ed models is not possible (see Cameron and Trivedi (2005), p.277). We solve this heuris- tically by adding one additional instrument (or more) and performing the Hansen’s J overiden- ti…cation test. We report the results of these tests in table A.8.
In the …rst four rows, we add one additional lag for each endogenous variable in the regression, leading to a degree of overidenti…cation of one. In the …fth row, we add one lag for all variables, leading to an overidenti…cation degree of four. Finally, we look at the instrument set of one lag from Arellano and Bond (1991). The instrument set consists of cross-products of the twice- lagged cash to asset ratio and year dummy variables. With a sample of 13 years, this gives a degree of overidenti…cation of 12.
We can see in this table that extending the amount of instruments, easily results in overiden- ti…cation. Therefore we use a parsimonious instrument set. In table 1 in our paper, we present the complete estimation results of the instrument set with two lags of the cash to asset ratio and one lag of all other endogenous variables. We will see that the results are quite similar to a fully identi…ed regresson.
Table A.8. Hansen’s J Tests for Overidenti…cation.
Instrument set extendend with H0:Model overidenti…cation
HansenJ statistic p-value Degrees of freedom
Cash/Assetsi;t 3 0.518 0.472 1
Long-term debt/Assetsi;t 2 4.274 0.039 1
Cap.expenditures/Assetsi;t 2 7.480 0.006 1
Net working cap./Assetsi;t 2 13.247 0.000 1
All endogenous var. two lags 29.664 0.000 4
Arellano and Bond (1991)-set for 1 lag 43.771 0.000 12
References
Anderson, T W. and Cheng Hsiao. 1982. "Estimation of Dynamic Models with Error Compo- nents." Journal of the American Statistical Association 76, 598-606.
Arellano, Manuel and Stephen Bond. 1991. "Some Tests of Speci…cation for Panel Data: Monte Carlo Evidence and an Application to Employment Equations." Review of Economic Studies, 58, 277-298.
Cameron, A. Colin, and Pravin K. Trivedi. 2005. Microeconometrics; methods and applications Hausman, Jerry A. "Speci…cation Test in Econometrics." Econometrica 46, 1251-1271.
TableA.3Correlationsinlevels(lowertraingle)and…rstdi¤erences(uppertriangle). Tablereportspairwisecorrelationsoflevelsand…rst-di¤erencesofmainvariablesusedthroughoutthepaper.Mostlevelvariableshave13,565observations(seetableA.2). Most…rst-di¤erencedvariableshave13,191variables.Thedataisunwinsorized.Forthe…rstfreecash‡owtoassetsmeasure,wemeasurefreecash‡owasthedi¤erence betweencash‡owandcapitalexpenditures.Forthesecondmeasure,wetakethedi¤erencebetweencash‡owanddepreciationtoassets.Formorevariablesdescriptions, seeappendixAandtableA.1. 1.2.3.4.5.6.7.8.9.10.11.12.13.14.15. 1.Cash/Assets---0.6600.7670.0060.0150.073-0.0210.0880.0000.0430.0480.0290.008-0.087-0.386 2.Cash/Sales0.714---0.508-0.015-0.0050.033-0.3940.1310.0000.0340.007-0.0090.015-0.051-0.262 3.log(Cash/Netassets)0.8470.561----0.010-0.0020.0550.0050.065-0.0010.0330.0630.0360.014-0.076-0.293 4.Cash‡ow/Assets0.0990.0350.064---0.9650.5950.1010.1360.007-0.045-0.346-0.094-0.1860.0050.092 5.Freecash‡ow/Assets0.1900.0980.1570.924---0.5760.0940.1550.014-0.052-0.333-0.081-0.1890.0020.080 6.Freecash‡ow/Assets0.2060.1050.2000.5470.646---0.015-0.0480.011-0.024-0.213-0.030-0.145-0.8010.086 7.log(Sales)-0.184-0.236-0.1960.016-0.013-0.045---0.4300.004-0.0480.0900.115-0.0500.0560.057 8.log(Assets)-0.195-0.076-0.259-0.019-0.056-0.1090.915---0.005-0.0290.1380.0640.0450.160-0.015 9.Market-to-bookratio0.0340.0160.0270.0510.0280.017-0.012-0.015---0.003-0.0030.003-0.005-0.0090.006 10.Industry0.0050.068-0.024-0.066-0.0460.084-0.162-0.1070.021---0.024-0.0310.054-0.004-0.024 11.Totaldebt/Assets-0.334-0.333-0.285-0.289-0.287-0.2400.3130.245-0.033-0.175---0.4810.3080.008-0.362 12.Short-termdebt/A.-0.163-0.291-0.086-0.241-0.161-0.0250.180-0.007-0.022-0.1370.742----0.685-0.032-0.739 13.Long-termdebt/A.-0.282-0.117-0.307-0.116-0.216-0.3210.2290.368-0.021-0.0820.520-0.186---0.0410.501 14.Capitalexp./Assets-0.157-0.093-0.1800.2050.025-0.7070.0660.1110.023-0.1540.037-0.1750.277----0.039 15.NetWorkingCap./A.0.0630.0750.1250.1180.1730.239-0.113-0.0970.0030.049-0.597-0.503-0.234-0.180---
