Quantitative Techniques ( use Eviews and Excel ) - Essay Example

? Problem 2: Monetary policy and Stock Market 2. a) To compute the GDP gap, we use the Hodrick-Prescott filter. Figure Figure 2 Figure 3 Figures 5-7 are the required graphs. We see that both the output gap as well as the inflation shows volatility. Interestingly both series show signs of a sharp dip around the 1st quarter of 2008 and then a late recovery during the last couple of quarters reflecting the global recession. The interest rate exhibits a volatile but generally downward trend until the 4th quarter of 2008 since when there has been a very sharp dip in the variable. This also reflects the attempts of expansionary monetary policy facing recession. 2.b) Table 1 Dependent Variable: I Method: Least Squares Date: 12/31/11 Time: 13:16 Sample (adjusted): 1990Q2 2010Q3 Included observations: 82 after adjustments Coefficient Std. Error t-Statistic Prob.   C 1.486055 0.105763 14.05076 0.0000 DLCPI 9.369895 9.630384 0.972951 0.3335 GAP 26.69825 6.550314 4.075873 0.0001 R-squared 0.215946     Mean dependent var 1.548800 Adjusted R-squared 0.196097     S.D. dependent var 0.765175 S.E. of regression 0.686061     Akaike info criterion 2.120198 Sum squared resid 37.18365     Schwarz criterion 2.208248 Log likelihood -83.92811     Hannan-Quinn criter. 2.155549 F-statistic 10.87919     Durbin-Watson stat 0.067376 Prob(F-statistic) 0.000067 Table 7 shows that only the output gap is significant in predicting the interest rate or the policy rate. Additionally, neither of the coefficients takes values that are close to 0.5. 2.c) The stated hypothesis implies that the policy rate responds identically to variations in the output gap and inflation. Table 2 Wald Test: Equation: Untitled Test Statistic Value   df     Probability F-statistic 10.39767 (2, 79)   0.0001 Chi-square 20.79535 2   0.0000 Null Hypothesis Summary: Normalized Restriction (= 0) Value   Std. Err. -0.5 + C(2) 8.869895 9.630384 -0.5 + C(3) 26.19825 6.550314 Restrictions are linear in coefficients. In table 7 we formally show that the coefficients are not equal to 0.5. The null hypothesis that both coefficients take the value 0.5 is rejected by the test. Figure 4 2.d) Figure 8 presents the predicted versus actual values of the policy rate and the fitted residuals. This graph gives a general idea of how well the model fits the data. 2.e) Table 3 Chow Breakpoint Test: 2001Q1  Null Hypothesis: No breaks at specified breakpoints Varying regressors: All equation variables Equation Sample: 1990Q2 2010Q3 F-statistic 26.00470 Prob. F(3,76) 0.0000 Log likelihood ratio 57.91748 Prob. Chi-Square(3) 0.0000 Wald Statistic  78.01409 Prob. Chi-Square(3) 0.0000 Table 9 shows that the chow breakpoints test reject the null hypothesis that there were no breaks at the 1st quarter of 2001. Thus, we conclude that there was a structural break in the relationship in the 1st quarter of 2001. 3.a) I will choose my model based on the principle of parsimony and information criterion. Higher values of AIC and SIC will imply including higher orders of k leads to a better model. Tables 10 through 14 present the results of running OLS regressions for the provided specification for k=0,1,2,3,4. The SIC has gone up with the inclusion of each additional lag. However, the AIC falls until the 2nd last specification. It increases and is higher compared to even the 1st specification (table 10) as is the SIC for the last specification (table 14). However, it should be noted that stock market value emerges as being significant only in the 1st specification. In all following specifications, neither the current period neither the lagged values of the variable are significant. But in these specifications, the gain in values of the information criterion are not substantially high. Table 4 Dependent Variable: I Method: Least Squares Date: 12/31/11 Time: 13:27 Sample (adjusted): 1990Q2 2010Q3 Included observations: 82 after adjustments Coefficient Std. Error t-Statistic Prob.   C 11.56005 1.809245 6.389434 0.0000 INFLATION_RATE -0.018618 0.083502 -0.222962 0.8241 GAP 37.42198 5.897804 6.345070 0.0000 S -1.192461 0.213913 -5.574513 0.0000 R-squared 0.439200     Mean dependent var 1.548800 Adjusted R-squared 0.417630     S.D. dependent var 0.765175 S.E. of regression 0.583929     Akaike info criterion 1.809475 Sum squared resid 26.59588     Schwarz criterion 1.926876 Log likelihood -70.18847     Hannan-Quinn criter. 1.856610 F-statistic 20.36231     Durbin-Watson stat 0.123508 Prob(F-statistic) 0.000000 Table 5 Dependent Variable: I Method: Least Squares Date: 12/31/11 Time: 13:29 Sample (adjusted): 1990Q2 2010Q3 Included observations: 82 after adjustments Coefficient Std. Error t-Statistic Prob.   C 11.89533 1.799543 6.610194 0.0000 INFLATION_RATE -0.051211 0.084790 -0.603971 0.5476 GAP 40.28127 6.073199 6.632629 0.0000 S 0.505000 1.031937 0.489371 0.6260 S(-1) -1.736566 1.033308 -1.680589 0.0969 R-squared 0.459042     Mean dependent var 1.548800 Adjusted R-squared 0.430940     S.D. dependent var 0.765175 S.E. of regression 0.577217     Akaike info criterion 1.797842 Sum squared resid 25.65485     Schwarz criterion 1.944593 Log likelihood -68.71151     Hannan-Quinn criter. 1.856760 F-statistic 16.33503     Durbin-Watson stat 0.165984 Prob(F-statistic) 0.000000 Table 6 Dependent Variable: I Method: Least Squares Date: 12/31/11 Time: 13:40 Sample (adjusted): 1990Q3 2010Q3 Included observations: 81 after adjustments Coefficient Std. Error t-Statistic Prob.   C 12.62083 1.813333 6.960015 0.0000 INFLATION_RATE -0.030399 0.093838 -0.323951 0.7469 GAP 42.55643 6.088557 6.989576 0.0000 S 0.104524 1.028211 0.101656 0.9193 S(-1) 0.387918 1.521842 0.254900 0.7995 S(-2) -1.813099 0.998446 -1.815921 0.0734 R-squared 0.478052     Mean dependent var 1.534596 Adjusted R-squared 0.443255     S.D. dependent var 0.758986 S.E. of regression 0.566320     Akaike info criterion 1.771871 Sum squared resid 24.05385     Schwarz criterion 1.949238 Log likelihood -65.76079     Hannan-Quinn criter. 1.843033 F-statistic 13.73849     Durbin-Watson stat 0.138208 Prob(F-statistic) 0.000000 Table 7 Dependent Variable: I Method: Least Squares Date: 12/31/11 Time: 13:39 Sample (adjusted): 1990Q4 2010Q3 Included observations: 80 after adjustments Coefficient Std. Error t-Statistic Prob.   C 12.96918 1.915252 6.771527 0.0000 INFLATION_RATE -0.039523 0.096237 -0.410683 0.6825 GAP 42.65119 6.283226 6.788103 0.0000 S -0.072178 1.050083 -0.068735 0.9454 S(-1) 0.384182 1.532661 0.250663 0.8028 S(-2) -0.701228 1.534027 -0.457116 0.6489 S(-3) -0.972658 1.019528 -0.954027 0.3432 R-squared 0.470634     Mean dependent var 1.520037 Adjusted R-squared 0.427125     S.D. dependent var 0.752306 S.E. of regression 0.569409     Akaike info criterion 1.794998 Sum squared resid 23.66855     Schwarz criterion 2.003425 Log likelihood -64.79991     Hannan-Quinn criter. 1.878562 F-statistic 10.81682     Durbin-Watson stat 0.117488 Prob(F-statistic) 0.000000 Table 8 Dependent Variable: I Method: Least Squares Date: 12/31/11 Time: 13:35 Sample (adjusted): 1991Q1 2010Q3 Included observations: 79 after adjustments Coefficient Std. Error t-Statistic Prob.   C 12.91743 2.044128 6.319289 0.0000 INFLATION_RATE -0.034212 0.099230 -0.344778 0.7313 GAP 41.84361 6.676451 6.267344 0.0000 S -0.094739 1.070665 -0.088486 0.9297 S(-1) 0.348611 1.554998 0.224188 0.8233 S(-2) -0.714034 1.555465 -0.459049 0.6476 S(-3) -0.402052 1.590093 -0.252848 0.8011 S(-4) -0.494418 1.048884 -0.471375 0.6388 R-squared 0.457128     Mean dependent var 1.505981 Adjusted R-squared 0.403606     S.D. dependent var 0.746466 S.E. of regression 0.576470     Akaike info criterion 1.831978 Sum squared resid 23.59458     Schwarz criterion 2.071922 Log likelihood -64.36313     Hannan-Quinn criter. 1.928107 F-statistic 8.540855     Durbin-Watson stat 0.121584 Prob(F-statistic) 0.000000 It is also important to note from tables that the values of the coefficient on the GDP gap as well as the intercept do not change much due to inclusion of the variable s representing the stock market value. Thus based on the principle of parsimony we conclude that only the current period stock market value along the GDP gap are significant determinants of the policy rate. 3.b) Now we turn to evaluating whether the assumptions of the CLRM model hold in the present case. Table 9 Heteroskedasticity Test: White F-statistic 3.766706     Prob. F(9,72) 0.0006 Obs*R-squared 26.24948     Prob. Chi-Square(9) 0.0019 Scaled explained SS 47.17564     Prob. Chi-Square(9) 0.0000 Table 15 presents the results of White’s heteroscedasticity test. Observe from the computed F statistic and the associated probability that the null of homoscedasticity is rejected. Now, to check the possibility of autocorrelation, we first graph the fitted residuals in figure 9 below. Figure 5 The figure above (9) contains evidence of persistence implying positive autocorrelation. Also, the Durbin Watson test statistic is equal to 0.121. Finally, as shown in table 13 the Breusch Godfrey serial correlation LM test also rejects the null hypothesis of no autocorrelation. Thus, we see that homoscedasticity and non-autocorrelation assumptions are violated here. Table 13 Breusch-Godfrey Serial Correlation LM Test: F-statistic 146.2548     Prob. F(4,76) 0.0000 Obs*R-squared 73.45683     Prob. Chi-Square(4) 0.0000 To evaluate the normality of the errors we plot the histogram of the fitted residuals and also compute the Jarque-Bera statistic which tests for normality using the kurtosis of the distribution. The histogram quite blatantly shows that there are deviations from normality evident here and the distribution seems to be skewed to the right. The Jarque-Bera statistic also rejects the normality of the errors. Thus, we finally conclude that three major assumptions of the CLRM namely: homoscedasticity, non-autocorrelation and finally normality are violated. Figure 6 3.c) Table 10 Dependent Variable: I Method: Least Squares Date: 12/31/11 Time: 15:18 Sample (adjusted): 1990Q3 2010Q3 Included observations: 81 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Coefficient Std. Error t-Statistic Prob.   C 0.545474 0.511956 1.065470 0.2902 INFLATION_RATE 0.099173 0.026313 3.769016 0.0003 GAP 6.345272 3.396854 1.967985 0.0488 S 0.320651 0.154492 2.075515 0.0415 D2008Q4 -0.632826 0.087217 -7.255737 0.0000 INFLATION_RATE(-1) -0.061917 0.022032 -2.810298 0.0064 GAP(-1) -7.130420 4.006989 -1.779496 0.0794 S(-1) -0.357884 0.158069 -2.264108 0.0266 I(-1) 0.788440 0.045425 7.35711 0.0000 R-squared 0.985860     Mean dependent var 1.534596 Adjusted R-squared 0.984289     S.D. dependent var 0.758986 S.E. of regression 0.095134     Akaike info criterion -1.762618 Sum squared resid 0.651636     Schwarz criterion -1.496568 Log likelihood 80.38604     Hannan-Quinn criter. -1.655876 F-statistic 627.4942     Durbin-Watson stat 2.102472 Prob(F-statistic) 0.000000 Table 14 above presents the results of the OLS regression where the heteroscedasticity has been accounted for by using White’s heteroscedasticity Consistent Standard errors, lagged values of the explanatory variables are included to account for the autocorrelation and finally, observing the sharp dip in the interest rate in the 4th quarter of 2008, we also include a dummy for that to correct for the non-normality. Observe that now the stock market value now is a significant determinant of the interest rate, it has a positive impact. Inflation, the GDP gap at current and lagged values is significant. It is interesting to note that while current period inflation and current period GDP gap both have positive effects on the interest rate, lagged values have a negative impact which is of course expected since interest rate is a policy variable which attempts to stabilize inflation and output. Note that lagged value of the interest rate itself also has a small but positive impact on the current period interest rate. Thus, it appears that interest rate follows a process that is partially autoregressive as well. Figure 7 The figure above presents the histogram of the residuals. Evidently, this histogram reflects patterns much closer to normalcy compared to the one obtained from the previous specification. 4. Finally, we turn to GMM estimation of the model. For instruments we use one period lagged value of inflation, gdp gap and stock market value. The results are presented in table 15. Table 11 Dependent Variable: I Method: Generalized Method of Moments Date: 12/31/11 Time: 15:18 Sample (adjusted): 1990Q2 2010Q3 Included observations: 82 after adjustments Kernel: Bartlett, Bandwidth: Fixed (3), No prewhitening Simultaneous weighting matrix & coefficient iteration Convergence achieved after: 1 weight matrix, 2 total coef iterations Instrument list: S(-1) INFLATION_RATE(-1) GAP(-1) Coefficient Std. Error t-Statistic Prob.   C 58.89989 8.308053 7.089493 0.0000 INFLATION_RATE -0.0182486 2.001259 -1.779496 0.0794 GDPGAP 38.25255 1.886529 5.434609 0.0000 S 0.560259 0.284907 1.966462 0.0528 R-squared 0.754179     Mean dependent var 1.548800 Adjusted R-squared 0.744725     S.D. dependent var 0.765175 S.E. of regression 0.386603     Sum squared resid 11.65801 Durbin-Watson stat 0.354732     J-statistic 1.83E-24 Comparing these results to those found in table 11, we find that the estimated coefficients have the same signs and significances and additionally, the values are quite close as well. Thus the interpretation remains almost identical as before. Problem 3: Financial constraints and investment cash- flow sensitivity 2. Table 16 presents the summary statistics for the entire sample while the tables 17 through 19 present summary statistics for each separate subsample categorized in terms of extent of financial constraint. Table 12 investment   cashflow   mtb   dividend   Mean 0.058747 Mean 0.146616 Mean 2.078205 Mean 0.192553 Standard Error 0.000616 Standard Error 0.003487 Standard Error 0.152406 Standard Error 0.002865 Median 0.044032 Median 0.140038 Median 1.462401 Median 0.073989 Mode 0.32 Mode 0.113372 Mode 1.243649 Mode 0 Standard Deviation 0.052698 Standard Deviation 0.298429 Standard Deviation 13.04383 Standard Deviation 0.24521 Sample Variance 0.002777 Sample Variance 0.08906 Sample Variance 170.1414 Sample Variance 0.060128 Kurtosis 7.265884 Kurtosis 3914.227 Kurtosis 6718.259 Kurtosis 0.630202 Skewness 2.365192 Skewness -58.224 Skewness 80.45994 Skewness 1.239276 Range 0.32 Range 22.17196 Range 1094.034 Range 1 Minimum 0 Minimum -21.2544 Minimum 0.294524 Minimum 0 Maximum 0.32 Maximum 0.917518 Maximum 1094.329 Maximum 1 Sum 430.324 Sum 1073.965 Sum 15222.85 Sum 1410.454 Count 7325 Count 7325 Count 7325 Count 7325 Table 17 presents summary statistics for highly constrained firms. Table 13 Investment   Cashflow   MTB   Dividend   Mean 0.061244 Mean 0.142752 Mean 2.24203 Mean 0.031966 Standard Error 0.000895 Standard Error 0.005537 Standard Error 0.244219 Standard Error 0.000852 Median 0.041901 Median 0.140833 Median 1.473216 Median 0 Mode 0.32 Mode 0.113372 Mode 1.243649 Mode 0 Standard Deviation 0.060443 Standard Deviation 0.374056 Standard Deviation 16.49882 Standard Deviation 0.057548 Sample Variance 0.003653 Sample Variance 0.139918 Sample Variance 272.2111 Sample Variance 0.003312 Kurtosis 5.334878 Kurtosis 2543.666 Kurtosis 4211.155 Kurtosis 1.101193 Skewness 2.152954 Skewness -47.4461 Skewness 63.79679 Skewness 1.602291 Range 0.32 Range 22.17196 Range 1094.034 Range 0.2 Minimum 0 Minimum -21.2544 Minimum 0.294524 Minimum 0 Maximum 0.32 Maximum 0.917518 Maximum 1094.329 Maximum 0.2 Sum 279.5168 Sum 651.5215 Sum 10232.62 Sum 145.8915 Count 4564 Count 4564 Count 4564 Count 4564 Table 18 presents the summary statistics for the medium constrained firms. Table 14 investment   cashflow   mtb   dividend   Mean 0.055057 Mean 0.164053 Mean 1.883473 Mean 0.29088 Standard Error 0.00105 Standard Error 0.001718 Standard Error 0.032143 Standard Error 0.001572 Median 0.046282 Median 0.155299 Median 1.575089 Median 0.28718 Mode 0.109652 Mode 0.124102 Mode - Mode 0.333333 Standard Deviation 0.038546 Standard Deviation 0.063068 Standard Deviation 1.180119 Standard Deviation 0.05773 Sample Variance 0.001486 Sample Variance 0.003978 Sample Variance 1.39268 Sample Variance 0.003333 Kurtosis 9.217613 Kurtosis 5.916238 Kurtosis 22.49154 Kurtosis -1.14969 Skewness 2.336392 Skewness 1.511686 Skewness 3.815303 Skewness 0.207554 Range 0.3173 Range 0.67787 Range 12.92397 Range 0.199878 Minimum 0.0027 Minimum -0.05004 Minimum 0.439787 Minimum 0.20004 Maximum 0.32 Maximum 0.627826 Maximum 13.36376 Maximum 0.399918 Sum 74.21686 Sum 221.1439 Sum 2538.921 Sum 392.1058 Count 1348 Count 1348 Count 1348 Count 1348 Table 19 presents the summary statistics for the subsample of low constrained firms. Table 19 investment   cashflow   mtb   dividend   Mean 0.054204 Mean 0.142462 Mean 1.734825 Mean 0.61745 Standard Error 0.000893 Standard Error 0.001999 Standard Error 0.030037 Standard Error 0.004185 Median 0.047213 Median 0.123954 Median 1.338803 Median 0.588608 Mode 0.032472 Mode 0.188894 Mode - Mode 0.444444 Standard Deviation 0.033575 Standard Deviation 0.075124 Standard Deviation 1.129106 Standard Deviation 0.157319 Sample Variance 0.001127 Sample Variance 0.005644 Sample Variance 1.27488 Sample Variance 0.024749 Kurtosis 7.139847 Kurtosis 18.5499 Kurtosis 11.95081 Kurtosis -0.70068 Skewness 1.971518 Skewness 3.18713 Skewness 3.087644 Skewness 0.542715 Range 0.293986 Range 0.85357 Range 8.891628 Range 0.599691 Minimum 0 Minimum 0.014662 Minimum 0.502669 Minimum 0.400309 Maximum 0.293986 Maximum 0.868232 Maximum 9.394297 Maximum 1 Sum 76.59031 Sum 201.2992 Sum 2451.308 Sum 872.4565 Count 1413 Count 1413 Count 1413 Count 1413 Comparing tables 16-19 we find that the means of investment and cashflow are not much different across the sub-samples. However, the market to book ratio and dividend payouts vary noticeably. While market to book ratio appears to be directly proportional to the degree of financial constraints, the dividend payouts understandably vary inversely with it. 3. Table 15 Test for Equality of Means Between Series Date: 12/31/11 Time: 15:18 Sample: 1998 2006 Included observations: 7952 Method df Value Probability Anova F-test (2, 21972) 1246.431 0.0000 Welch F-test* (2, 13796) 810.1169 0.0000 *Test allows for unequal cell variances Category Statistics Std. Err. Variable Count Mean Std. Dev. of Mean LCINV 7325 0.010456 0.025977 0.000304 MCINV 7325 0.010138 0.026993 0.000315 HCINV 7325 0.038153 0.056190 0.000657 All 21975 0.019582 0.041141 0.000278 In table 20 above, we test for differences across the mean investments for the three subsamples. The lower half of the table presents the investment means for low constrained medium constrained and high constrained firms (LCINV, MCINV and HCINV respectively). We find that although there are not much differences in the means of the low constrained and medium constrained groups investment means, the investment mean of the high constrained firm appears to be almost 4 times larger than these. This is further confirmed by the computed F-statistic in the upper half of the table which rejects the null of equal means across the three groups. 4. a) The advantages of running a panel technique over that of a pooled model are threefold: Panel techniques can account for heterogeneity across individual units but such heterogeneity is assumed away in pooled regressions. Panel techniques can account for time invariant omitted variables which can be the result of using a pooled data set. Autocorrelation and multicollinearity related problems are likely to be less manifested as compared to the situation when a pooled regression is used. 4. b) The equation would simply be rewritten by subtracting the group mean value from each of the variables of the group (mean centering). We would then run an OLS regression on concatenated data. Table 21 presents the results of the pooled regression. Observe that all the included explanatory variables are significant. From the signs of the coefficients we see that while cashflow and MTB affect the investment positively, dividend has a negative influence. Table 16 Dependent Variable: INVESTMENT Method: Panel Least Squares Date: 12/31/11 Time: 15:18 Sample: 1998 2006 Periods included: 9 Cross-sections included: 1017 Total panel (unbalanced) observations: 7325 Coefficient Std. Error t-Statistic Prob.   C 0.050491 0.001036 48.72999 0.0000 CASHFLOW 0.051625 0.003660 14.10363 0.0000 MTB 0.001237 8.38E-05 14.77451 0.0000 DIVIDEND -0.009786 0.002471 -3.960326 0.0001 R-squared 0.032545     Mean dependent var 0.058747 Adjusted R-squared 0.032149     S.D. dependent var 0.052698 S.E. of regression 0.051844     Akaike info criterion -3.080619 Sum squared resid 19.67719     Schwarz criterion -3.076852 Log likelihood 11286.77     Hannan-Quinn criter. -3.079324 F-statistic 82.09224     Durbin-Watson stat 0.443609 Prob(F-statistic) 0.000000 Tables 22 through 24 present pooled regressions for the individual subsamples. Table 17 Dependent Variable: HCINV Method: Panel Least Squares Date: 12/31/11 Time: 15:18 Sample: 1998 2006 Periods included: 9 Cross-sections included: 1017 Total panel (unbalanced) observations: 7325 Coefficient Std. Error t-Statistic Prob.   C 0.022281 0.000732 30.42123 0.0000 HCCF 0.113095 0.003407 33.19108 0.0000 HCD 0.114108 0.012825 8.897643 0.0000 HCM 0.002539 7.85E-05 32.33464 0.0000 R-squared 0.167534     Mean dependent var 0.038153 Adjusted R-squared 0.167193     S.D. dependent var 0.056190 S.E. of regression 0.051278     Akaike info criterion -3.102572 Sum squared resid 19.24993     Schwarz criterion -3.098805 Log likelihood 11367.17     Hannan-Quinn criter. -3.101277 F-statistic 491.1169     Durbin-Watson stat 0.615588 Prob(F-statistic) 0.000000 From table 22 we see that for the highly constrained firms, all three variables have a positive influence. However, all explanatory variables have larger effects compared to the overall effects computed for the aggregated sample in table 21. Finally, note that for high constrained firms dividends actually have a positive impact contrary to the negative effect found to hold for the overall aggregated sample. Table 18 Dependent Variable: MCINV Method: Panel Least Squares Date: 12/31/11 Time: 15:18 Sample: 1998 2006 Periods included: 9 Cross-sections included: 1017 Total panel (unbalanced) observations: 7325 Coefficient Std. Error t-Statistic Prob.   C 0.000230 0.000209 1.099816 0.2714 MCCF 0.261884 0.009042 28.96394 0.0000 MCD 0.083550 0.003815 21.89799 0.0000 MCM -0.007147 0.000521 -13.71135 0.0000 R-squared 0.640346     Mean dependent var 0.010138 Adjusted R-squared 0.640198     S.D. dependent var 0.026993 S.E. of regression 0.016192     Akaike info criterion -5.408111 Sum squared resid 1.919314     Schwarz criterion -5.404344 Log likelihood 19811.21     Hannan-Quinn criter. -5.406816 F-statistic 4344.884     Durbin-Watson stat 1.208544 Prob(F-statistic) 0.000000 Table 23 above presents the results of the regression for the subsample of medium constrained firms. Observe that cashflow and dividends have larger impacts for medium firms compared to the aggregate sample. MTB however has a negative impact in the subsample contrary to the positive effect found in the overall sample. The cashflow effect for medium firms is larger than the high constrained firms while the dividends have a smaller effect. Interestingly MTB has a negative impact for these medium constrained firms. Table 19 Dependent Variable: LCINV Method: Panel Least Squares Date: 12/31/11 Time: 15:18 Sample: 1998 2006 Periods included: 9 Cross-sections included: 1017 Total panel (unbalanced) observations: 7325 Coefficient Std. Error t-Statistic Prob.   C 0.000431 0.000196 2.201588 0.0277 LCCF 0.092919 0.007758 11.97662 0.0000 LCD 0.060856 0.001202 50.62924 0.0000 LCM 0.000667 0.000533 1.250021 0.2113 R-squared 0.660649     Mean dependent var 0.010456 Adjusted R-squared 0.660510     S.D. dependent var 0.025977 S.E. of regression 0.015136     Akaike info criterion -5.542945 Sum squared resid 1.677214     Schwarz criterion -5.539177 Log likelihood 20305.04     Hannan-Quinn criter. -5.541650 F-statistic 4750.841     Durbin-Watson stat 0.999042 Prob(F-statistic) 0.000000 Table 24 presents the results of the regression in the final subsample: that for the low constrained firms. Observe that the cashflow and dividend effects are smaller for low constrained firms compared to both high and medium constrained firms. The effect of MTB is insignificant for these firms. 4. c) Table 25 below presents the results of running a fixed effects regression on the entire sample and table 26 presents results of fixed effects regressions where we account for degree of financial constraints by using interaction terms composed of the financial constraint dummies and the explanatory variables cash flow, dividend and MTB. Table 20 Dependent Variable: INVESTMENT Method: Panel Least Squares Date: 12/31/11 Time: 15:18 Sample: 1998 2006 Periods included: 9 Cross-sections included: 1017 Total panel (unbalanced) observations: 7325 Coefficient Std. Error t-Statistic Prob.   C 0.056413 0.000829 68.05029 0.0000 CASHFLOW 0.019159 0.002600 7.368034 0.0000 DIVIDEND -0.009130 0.002870 -3.181011 0.0015 MTB 0.000617 5.55E-05 11.11982 0.0000 Effects Specification Cross-section fixed (dummy variables) Period fixed (dummy variables) R-squared 0.725534     Mean dependent var 0.058747 Adjusted R-squared 0.680771     S.D. dependent var 0.052698 S.E. of regression 0.029774     Akaike info criterion -4.060872 Sum squared resid 5.582391     Schwarz criterion -3.092650 Log likelihood 15900.94     Hannan-Quinn criter. -3.727998 F-statistic 16.20815     Durbin-Watson stat 1.431919 Prob(F-statistic) 0.000000 Although accounting for time and firm level fixed effects dampens the values of the coefficients, we find that the signs and the significances are same as those obtained in the pooled regression for the entire sample. Thus, our final interpretation of the results remains the same as the interpretation of results in table 21. We conclude that while cash flow and MTB contribute positively to investment, dividend has a negative impact. Table 21 Dependent Variable: INVESTMENT Method: Panel Least Squares Date: 12/31/11 Time: 15:18 Sample: 1998 2006 Periods included: 9 Cross-sections included: 1017 Total panel (unbalanced) observations: 7325 Coefficient Std. Error t-Statistic Prob.   HCCF 0.160487 0.003474 46.19608 0.0000 MCCF 0.262232 0.032807 7.993246 0.0000 LCCF 0.093400 0.030120 3.100935 0.0019 HCD 0.202611 0.014319 14.15011 0.0000 MCD 0.084160 0.013705 6.140750 0.0000 LCD 0.061377 0.004577 13.41098 0.0000 HCM 0.003539 8.17E-05 43.29520 0.0000 MCM -0.007153 0.001892 -3.780170 0.0002 LCM 0.000679 0.002071 0.327776 0.7431 R-squared -0.242987     Mean dependent var 0.058747 Adjusted R-squared -0.244346     S.D. dependent var 0.052698 S.E. of regression 0.058784     Akaike info criterion -2.828650 Sum squared resid 25.28127     Schwarz criterion -2.820173 Log likelihood 10368.93     Hannan-Quinn criter. -2.825736 Durbin-Watson stat 0.668598 The results in table 26 comply with the results obtained for the pooled regressions for the subsamples presented in tables 22 through 24. Thus the only difference that emerges in the fixed effects regressions compared to the pooled regression is that the inclusion of the time and firm level fixed effects dampens the coefficients slightly. However, the signs and significances remain unchanged. 4. d) In table 27 we test for differences across the coefficients of cashflow for the subsamples. A Wald test for parameter restrictions is employed. Table 22 Wald Test: Equation: Untitled Test Statistic Value   df     Probability F-statistic 10.66342 (2, 7315)   0.0000 Chi-square 21.32684 2   0.0000 Null Hypothesis Summary: Normalized Restriction (= 0) Value   Std. Err. C(2) - C(4) 0.016045 0.026704 C(3) - C(4) 0.148771 0.039194 Restrictions are linear in coefficients. The null hypothesis is that the coefficients of cash flow is identical for high, medium and low constrained firms or, C(2) = C(3) = C(4). The table shows that the computed f statistic is 10.66 which is greater than the critical value and the probability is thus 0.00. Therefore, the null hypothesis is rejected implying that the effect of cashflow on investment is not the same for firms operating with different levels of financial constraints. 5) Figure 8 Figure 11 plots the coefficients of cashflow for high medium and low constrained firms. We find that the cashflow sensitivity is the highest for the medium constrained firms. Although we see that it is higher for highly constrained firms than the lower constrained firms, the finding that it is highest for the medium constrained firms invalidates the monotonicity principle. Read More