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The Impact of Interest Rate Spread and Money Supply (M2) on Economic Growth – A Study in 40 Selected Nations
- Quy T. Vo
- Mai. H. T. Tran
- 1290-1306
- Aug 14, 2023
- Social Science
The Impact of Interest Rate Spread and Money Supply (M2) on Economic Growth – A Study in 40 Selected Nations
Quy T. Vo1,2,*, Mai. H. T. Tran1,2
1International University, Ho Chi Minh City, Vietnam
2Vietnam National University, Ho Chi Minh City, Vietnam
*Corresponding author
DOI: https://dx.doi.org/10.47772/IJRISS.2023.70803
Received: 26 June 2023; Revised: 14 July 2023; Accepted: 17 July 2023; Published: 14 August 2023
ABSTRACT
The goal of this research study is to look at how the Interest Rate Spread and Money Supply (M2) affect Economic Growth in different countries. We evaluate the literature on conducting research to investigate the impact of independent variables and control variables on economic growth. The research spans 40 countries from 2001 to 2021 and is divided into three groups: Developed Countries, Developing Countries, and Emerging Countries. The findings confirmed that the Interest Rate Spread and Money Supply (M2) have a positive impact on Economic Growth. These results imply that expantaionary mometery policy supports economic growth. The positive relationship between interest rate spread and economic growth confirmed the the importance of the banking sector in the economy.
Keywords: Interest Rate Spread, Money Supply (M2), Economic Growth
INTRODUCTION
Most central banks have used monetary policy as a tool to support economic growth. Changing the money supply will affect the inflation rate and then interest rates in debts markets, both borrowing and lending rates, and finally cause prices to change. Therefore, changes in the money supply can affect the production of goods and services level in the economy. This is why monetary policy is a meaningful policy tool for achieving both inflation and growth objectives. The global economy has been experiencing the hard time: Russia’s invasion of Ukraine, inlation rate increasing in most economies and reaching the highest level for the decade. The central banks have applied an appropriate monetary policy to control inflation rate and gain expected economic growth rate. The situation motivated us to conduct the study to investigate the impact of money supply and interest rate spread on economic growth. The next section of the paper will be literature review, hypothesis development and research model, data processing, research findings and discussion and conclusion.
The neoclassical growth framework, and monetarist theory are theoretical frameworks providing insights into the connection between IRS, M2, and economic growth. However, there is still ambiguous agreement of the relationship between IRS, money supply (M2), and economic growth in previous studies. Obeng & Sakyi (2017) confirmed significantly impact of macroeconomic factors on IRS in the long run in Ghana. On other side, IRS impacts economic growth significantly and negatively both in the short and long term, according to Daniel, et al. (2022). Regarding the relationship between money supply (M2) and economic growth, according to Nyorekwa et. al., (2018), emerging nations with undeveloped financial systems have limited connectivity to the global market likely to have a weaker link between monetary policy and economic growth. However, Manouchehr & Ahmad (2011) confirmed a substantial correlation between M2 and gross domestic product in Iran. Most studies on the same research issue conducted in single economy, therefore the correlation between IRS, M2, and economic growth across various economies should be further investigated. This study tries to fill the gap by conducting the study with 40 countries in different groups of economies: emerging market economies, developing countries, and developed countries to provide meaningful empirical evidence to get insights of the relaionship.
LITERATURE REVIEW
The difference between lending rates and deposit rates of financial institutions is known as an interest rate spread. Monetarist theory introduced by Friedman (1968) highlights the importance of money supply as an important macroeconomic factor affecting the economic growth of a country. Monetarist theory states that changes in money supply have the greatest effect on both the pattern of the business cycle and the growth rate of the economy (Kenton, 2021).
Interest Rate Spread and economic growth
IRS is usually used as a measure of bank efficiency (Mohamed, Jalloh, & Yao, 2017). A considerable disparity between loan and deposit rates reflects a weak and ineffective financial sector that might limit economic growth and promote instability according to Cochrane (2013), High IRS, on the other hand, is one of the key drivers of delayed economic growth in developing economies (Leimbach, 2015).
Money Supply (M2) and economic growth
Chaitip et. al., (2015) employed the Pooled Mean Group Estimator (PMGE) to investigate the link between money supply and economic development in ASEAN Economic Cooperation (AEC) countries between 1995 and 2013. Their findings revealed that the money supply support economic growth. Inam (2017) investigated the impact of monetary policy on Nigeria’s economic development from 1970 to 2012 by using the Ordinary Least Squares (OLS) approach and the Granger Causality test. The analysis showed a statistically negligible positive correlation between the money supply and economic growth. Aslam (2016) investigated the influence of the money supply on the Sri Lankan economy from 1959 to 2013. The findings revealed a considerable positive effect of the money supply on economic growth at a 1% level of significance.
Hypothesis development and research model
Based on the theories and empirical evidence presented above, we propose the following research hypotheses:
H1: Interest rate spread has a positive influence on economic growth in the selected countries.
H2: Money supply (M2) has a positive influence on economic growth in the selected countries.
To test above research hypotheses, we proposed the research model as below:
αi: The regression intercept.
βi: The regression slopes.
εi,t: The random error of the listed country i at the end of quarter t
Table 1 – Variables description
Data processing
Data is yearly data point collected from 2001 to 2021. The research sample consists of 40 countries listing in Appendix 1 with 840 observations. The Generalized Least Squares (GLS) regression model was used to test research hypotheses. Table 2 presents statistical despription of all variables in the research model. Table 3 shows the result of the autocorrelation test.
Statistical description
Table 2 – Descriptive statistics
Variable | Mean | Std. Dev. | Min | Max |
GDP | 3.26 | 3.94 | (21.4) | 15.33 |
IRS | 7.01 | 6.24 | (0.68) | 45.11 |
M2 | 0.14 | 0.73 | (0.57) | 14.62 |
SAV | 19.70 | 1.73 | (21.19) | 57.06 |
INF | 5.44 | 8.92 | (11.16) | 150 |
EXP | 35.33 | 21.7 | 6.47 | 115.37 |
FDI | 3.90 | 6.63 | (40.08) | 106.6 |
Correlation testing
Table 3 shows the correlation coefficient between variables in the research model. The test confirmed that the autocorrelation phenominon does not exist in the data set because all the correlation coefficient values are lower than 0.4.
Table 3 – Correlation matrix
GDP | IRS | M2 | SAV | INF | EXP | FDI | |
GDP | 1 | ||||||
IRS | 0.0309 | 1 | |||||
M2 | 0.0501 | 0.0413 | 1 | ||||
SAV | 0.1534 | -0.1381 | -0.0211 | 1 | |||
INF | -0.0393 | 0.1036 | 0.0009 | -0.1282 | 1 | ||
EXP | 0.0269 | -0.1827 | 0.0791 | 0.2937 | -0.0045 | 1 | |
FDI | 0.0332 | -0.0315 | 0.0168 | -0.0726 | 0.0193 | 0.3208 | 1 |
Multicollinearity test with Variance Inflation Factor (VIF)
To get the effective regression coefficient, a multicollinearity test was conducted and resulted in VIF value lower than 3. The Multicollinearity Test results indicate a mean Variance Inflation Factor (VIF) of 1.12. This suggests that there is a moderate level of correlation among the independent variables in the regression model. While a VIF between 1 and 5 suggests some degree of multicollinearity, it is not severe enough to warrant immediate corrective measures. The relatively low VIF value indicates that the independent variables in the model are not highly correlated with each other. This is a positive finding as it ensures that the variables provide unique and independent information to the regression analysis. The absence of severe multicollinearity enhances the reliability of the estimated coefficients and allows for more accurate interpretation and inference.
Table 4 – VIF test for multicollinearity
Variable | VIF | 1/VIF |
EXP | 1.3 | 0.770330 |
SAV | 1.16 | 0.861130 |
FDI | 1.15 | 0.866173 |
IRS | 1.06 | 0.947459 |
INF | 1.03 | 0.973606 |
M2 | 1.01 | 0.988354 |
Mean VIF | 1.12 |
RESEARCH FINDINGS
Table 5 presents the result of hypothesis testing by applying GLS (Generalized Least Squares) regression model. The GLS regression model provides reliable coefficient estimates with statistically significant relationships between the GDP growth rate and the independent variables with p-values lower than 0.05. The results confirmed that H1 and H2 are accepted. In other words, interest rate spread and money supply are explaining factors of the GDP growth rate.
Table 5 – The testing result for the hypothesis
GDP | Coef. | Std. Err. | z | P>z | [95% Conf. | Interval] |
IRS | 0.0335039 | 0.006985 | 4.8 | 0.000 | 0.0198137 | 0.0471942 |
M2 | 0.3041052 | 0.0244833 | 12.42 | 0.000 | 0.2561188 | 0.3520916 |
SAV | 0.0609564 | 0.0034468 | 17.68 | 0.000 | 0.0541907 | 0.0677018 |
INF | -0.0089334 | 0.0031387 | -2.85 | 0.004 | -0.0150852 | -0.0027816 |
EXP | -0.0059354 | 0.0019309 | -3.07 | 0.002 | -0.0097199 | -0.0021508 |
FDI | 0.025167 | 0.0057106 | 4.43 | 0.000 | 0.0141241 | 0.0365093 |
_cons | 1.863495 | 0.1620476 | 11.50 | 0.000 | 1.545888 | 2.181103 |
In addition, the coefficient estimates for the GDP growth rate variable with IRS, M2 growth rate, gross domestic savings, and foreign direct investment variables have t-statistics greater than 1.96 providing empirical evidence of a significant relationship between these variables in the research model. The coefficient estimate for the GDP growth rate and inflation rate variable has a t-statistic below 1.96 suggesting that the relationship is not statistically significant.
CONCLUSIONS AND RECOMMENDATIONS
This study conducted aims to investigate the impact of interest rate spread and money supply (M2) on economic growth across various countries. By utilizing the GLS regression model, valuable insights into the associations between these variables were gained. The analysis of the data revealed a statistically significant relationship between the IRS, money supply (M2), and economic growth in the selected 40 countries. These findings further validate the substantial influence of interest rate spread and money supply (M2) on economic growth across different countries, providing empirical evidence of their important role in driving economic growth dynamics. The study’s findings imply that the central banks may use IRS and M2 as tools to gain expected economic growth rate.
In conclusion, this study provided empirical evidence of the impact of interest rate spread and money supply (M2) on economic growth in various countries. The findings substantiate the importance of these factors in shaping economic performance. The indings also provide recommendations to policymakers, investors, and financial analysts in making well-informed decisions That Foster Sustainable Economic Growth And Stability./.
REFERENCES
- Aslam, A. L. (2016, 03). Impact of Money Supply on Sri Lankan Economy: An Econometric Analysis. International Letters of Social and Humanistic Sciences, 67, 11-17. doi:10.18052/www.scipress.com/ILSHS.67.11
- Chaitip, P., Chokethaworn, K., Chaiboonsri, C., & Khounkhalax, M. (2015, 12). Money Supply Influencing on Economic Growth-wide Phenomena of AEC Open Region. Procedia Economics and Finance, 24, 108-115. doi:10.1016/S2212-5671(15)00626-7
- Cochrane, J. H. (2013, 05). Finance: Function Matters, Not Size. Journal of Economic Perspectives, 27, 29-50. doi:https://www.aeaweb.org/articles?id=10.1257/jep.27.2.29
- Daniel, B., Paul, H., & Edmond, A. (2022). The Effect Of Interest Rate Spread On Economic Growth: Ghana’s Perspective. International Journal of Business and Management Review, 1-23.
- Friedman, M. (1968). The Role of Monetary Policy. The American Economic Review, 58, 1-17.
- Inam, U. S. (2017). Monetary Policy And Economic Growth In Nigeria: Evidence From Nigeria. Advances in Social Sciences Research Journal. doi:https://doi.org/10.14738/assrj.46.2806
- Kenton, W. (2021, 03 21). Monetarist Theory: Economic Theory of Money Supply. From Investopedia: https://www.investopedia.com/terms/m/monetaristtheory.asp
- Leimbach, M. a. (2015, 03). Future growth patterns of world regions – A GDP scenario approach. Global Environmental Change, 42. doi:10.1016/j.gloenvcha.2015.02.005
- Manouchehr, N., & Ahmad, J. S. (2011). The Impact of Monetary Policy on Economic Growth in Iran. Middle-East Journal of Scientific Research, 740-743.
- Mohamed, Jalloh, & Yao, G. (2017, 01). Financial Deepening, Interest Rate Spread and Economic Growth: New Evidence from Sub-Sahara Africa. International Journal of Business, Economics and Management, 4, 52-64. doi:10.18488/journal.62.2017.43.52.64
- Nyorekwa, T., Enock, Odhiambo, & Nicholas. (2018, 05). Monetary Policy and Economic Growth: A Review of International Literature. Journal of Central Banking Theory and Practice, 7, 123-237. doi:10.2478/jcbtp-2018-0015
- Obeng, S., & Sakyi, D. (2017, 03). Macroeconomic Determinants of Interest Rate Spreads in Ghana. African Journal of Economic and Management Studies, 8, 76-88. doi:10.1108/AJEMS-12-2015-0143
APPENDIX
Appendix 1 – List Of Countries
No. | Name | Region | Income Group | Note |
DEVELOPED COUNTRIES | ||||
1 | United States | North America | High income | The list is based on the G7. The G7 is an informal grouping of seven of the world’s advanced economies, including Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States, as well as the European Union. |
2 | France | Europe & Central Asia | High income | |
3 | Germany | Europe & Central Asia | High income | |
4 | Italy | Europe & Central Asia | High income | |
5 | Japan | East Asia & Pacific | High income | |
6 | United Kingdom | Europe & Central Asia | High income | |
7 | Canada | North America | High income | |
EMERGING COUNTRIES | ||||
8 | Brazil | Latin America & Caribbean | Upper middle income | |
9 | Chile | Latin America & Caribbean | High income | |
10 | China | East Asia & Pacific | Upper middle income | |
11 | Colombia | Latin America & Caribbean | Upper middle income | |
12 | Czechia | Europe & Central Asia | High income | |
13 | Egypt, Arab Rep. | Middle East & North Africa | Lower middle income | |
14 | Hungary | Europe & Central Asia | High income | |
15 | Indonesia | East Asia & Pacific | Lower middle income | |
16 | Korea, Rep. | East Asia & Pacific | High income | |
17 | Malaysia | East Asia & Pacific | Upper middle income | |
18 | Mexico | Latin America & Caribbean | Upper middle income | |
19 | Peru | Latin America & Caribbean | Upper middle income | |
20 | Philippines | East Asia & Pacific | Lower middle income | |
21 | South Africa | Sub-Saharan Africa | Upper middle income | |
DEVELOPING COUNTRIES | ||||
22 | Albania | Europe & Central Asia | Upper middle income | |
23 | Algeria | Middle East & North Africa | Lower middle income | |
24 | Antigua and Barbuda | Latin America & Caribbean | High income | |
25 | Armenia | Europe & Central Asia | Upper middle income | |
26 | Dominican Republic | Latin America & Caribbean | Upper middle income | |
27 | Eswatini | Sub-Saharan Africa | Lower middle income | |
28 | Guatemala | Latin America & Caribbean | Upper middle income | |
29 | Jamaica | Latin America & Caribbean | Upper middle income | |
30 | Jordan | Middle East & North Africa | Upper middle income | |
31 | Kenya | Sub-Saharan Africa | Lower middle income | |
32 | Nigeria | Sub-Saharan Africa | Lower middle income | |
33 | Paraguay | Latin America & Caribbean | Upper middle income | |
34 | Seychelles | Sub-Saharan Africa | High income | |
35 | Ukraine | Europe & Central Asia | Lower middle income | |
36 | Vietnam | East Asia & Pacific | Lower middle income | |
37 | Gambia | Sub-Saharan Africa | Low income | |
38 | Uganda | Sub-Saharan Africa | Low income | |
39 | Pakistan | South Asia | Lower middle income | |
40 | Lebanon | Middle East & North Africa | Lower middle income |
Appendix 2 – Stationarity Test of GDP Growth Rate Variable
Levin-Lin-Chu unit-root test for GDP
————————————
Ho: Panels contain unit roots Number of panels = 40
Ha: Panels are stationary Number of periods = 21
AR parameter: Common Asymptotics: N/T -> 0
Panel means: Included
Time trend: Not included
ADF regressions: 1 lag
LR variance: Bartlett kernel, 8.00 lags average (chosen by LLC)
—————————————————————————–
Statistic p-value
—————————————————————————–
Unadjusted t -15.5172
Adjusted t* -3.9807 0.0000
—————————————————————————–
Appendix 3 – Stationarity Test of Interest Rate Spread Variable
Levin-Lin-Chu unit-root test for IRS
————————————
Ho: Panels contain unit roots Number of panels = 40
Ha: Panels are stationary Number of periods = 21
AR parameter: Common Asymptotics: N/T -> 0
Panel means: Included
Time trend: Not included
ADF regressions: 1 lag
LR variance: Bartlett kernel, 8.00 lags average (chosen by LLC)
—————————————————————————–
Statistic p-value
—————————————————————————–
Unadjusted t -12.1698
Adjusted t* -4.9932 0.0000
—————————————————————————–
Appendix 4- Stationarity Test of M2 (Money Supply) Growth Rate Variable
Levin-Lin-Chu unit-root test for M2
———————————–
Ho: Panels contain unit roots Number of panels = 40
Ha: Panels are stationary Number of periods = 21
AR parameter: Common Asymptotics: N/T -> 0
Panel means: Included
Time trend: Not included
ADF regressions: 1 lag
LR variance: Bartlett kernel, 8.00 lags average (chosen by LLC)
—————————————————————————–
Statistic p-value
—————————————————————————–
Unadjusted t -18.0416
Adjusted t* 1.5356 0.9377
—————————————————————————–
Appendix 5 – Stationarity Test of Gross Domestic Savings Variable
Levin-Lin-Chu unit-root test for SAV
————————————
Ho: Panels contain unit roots Number of panels = 40
Ha: Panels are stationary Number of periods = 21
AR parameter: Common Asymptotics: N/T -> 0
Panel means: Included
Time trend: Not included
ADF regressions: 1 lag
LR variance: Bartlett kernel, 8.00 lags average (chosen by LLC)
—————————————————————————–
Statistic p-value
—————————————————————————–
Unadjusted t -10.6618
Adjusted t* -2.9478 0.0016
—————————————————————————–
Appendix 6 – Stationarity Test of Inflation Rate Variable
Levin-Lin-Chu unit-root test for INF
————————————
Ho: Panels contain unit roots Number of panels = 40
Ha: Panels are stationary Number of periods = 21
AR parameter: Common Asymptotics: N/T -> 0
Panel means: Included
Time trend: Not included
ADF regressions: 1 lag
LR variance: Bartlett kernel, 8.00 lags average (chosen by LLC)
—————————————————————————–
Statistic p-value
—————————————————————————–
Unadjusted t -14.8588
Adjusted t* -4.2883 0.0000
—————————————————————————–
Appendix 7 – Stationarity Test of Total Exports Variable
Levin-Lin-Chu unit-root test for EXP
————————————
Ho: Panels contain unit roots Number of panels = 40
Ha: Panels are stationary Number of periods = 21
AR parameter: Common Asymptotics: N/T -> 0
Panel means: Included
Time trend: Not included
ADF regressions: 1 lag
LR variance: Bartlett kernel, 8.00 lags average (chosen by LLC)
—————————————————————————–
Statistic p-value
—————————————————————————–
Unadjusted t -8.3767
Adjusted t* -2.7073 0.0034
—————————————————————————–
Appendix 8 – Stationarity Test of Foreign Direct Investment Variable
Levin-Lin-Chu unit-root test for FDI
————————————
Ho: Panels contain unit roots Number of panels = 40
Ha: Panels are stationary Number of periods = 21
AR parameter: Common Asymptotics: N/T -> 0
Panel means: Included
Time trend: Not included
ADF regressions: 1 lag
LR variance: Bartlett kernel, 8.00 lags average (chosen by LLC)
—————————————————————————–
Statistic p-value
—————————————————————————–
Unadjusted t -15.3111
Adjusted t* -7.1352 0.0000
—————————————————————————–
Appendix 9 – Pooled OLS Regression Model
Source | SS df MS Number of obs = 840
————-+—————————— F( 6, 833) = 4.71
Model | 427.19149 6 71.1985817 Prob > F = 0.0001
Residual | 12604.7411 833 15.131742 R-squared = 0.0328
————-+—————————— Adj R-squared = 0.0258
Total | 13031.9325 839 15.5326967 Root MSE = 3.89
—————————————————————————–
GDP | Coef. Std. Err. t P>|t| Beta
————-+—————————————————————
IRS | .0315285 .0220843 1.43 0.154 .0499782
M2 | .2878275 .1836052 1.57 0.117 .0537318
SAV | .0584744 .0123408 4.74 0.000 .1739913
INF | -.0104223 .0152648 -0.68 0.495 -.0235788
EXP | -.006975 .0070504 -0.99 0.323 -.0384087
FDI | .0352121 .0217631 1.62 0.106 .059239
_cons | 2.015293 .3840908 5.25 0.000 .
—————————————————————————–
Appendix 10 – Heteroscedasticity Test for Pooled OLS Regression Model
White’s test for Ho: homoskedasticity
against Ha: unrestricted heteroskedasticity
chi2(27) = 101.43
Prob > chi2 = 0.0000
Cameron & Trivedi’s decomposition of IM-test
—————————————————
Source | chi2 df p
———————+—————————–
Heteroskedasticity | 101.43 27 0.0000
Skewness | 40.14 6 0.0000
Kurtosis | 6.81 1 0.0090
———————+—————————–
Total | 148.38 34 0.0000
—————————————————
Appendix 11 – FEM Regression Model
Fixed-effects (within) regression Number of obs = 840
Group variable: country1 Number of groups = 40
R-sq: within = 0.0862 Obs per group: min = 21
between = 0.0075 avg = 21.0
overall = 0.0204 max = 21
F(6,794) = 12.49
corr(u_i, Xb) = -0.7023 Prob > F = 0.0000
—————————————————————————–
GDP | Coef. Std. Err. t P>|t| [95% Conf. Interval]
————-+—————————————————————
IRS | .148236 .050407 2.94 0.003 .0492892 .2471828
M2 | .1308447 .1658913 0.79 0.431 -.1947926 .456482
SAV | .1503282 .0320581 4.69 0.000 .0873994 .2132569
INF | -.0439006 .0147292 -2.98 0.003 -.0728133 -.0149878
EXP | .0570777 .0176556 3.23 0.001 .0224205 .0917349
FDI | .0341773 .021153 1.62 0.107 -.0073452 .0756998
_cons | -2.667113 .7882859 -3.38 0.001 -4.214483 -1.119742
————-+—————————————————————
Appendix 12 – REM Regression Model
Random-effects GLS regression Number of obs = 840
Group variable: country1 Number of groups = 40
R-sq: within = 0.0794 Obs per group: min = 21
between = 0.0122 avg = 21.0
overall = 0.0260 max = 21
Wald chi2(6) = 45.46
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
—————————————————————————–
GDP | Coef. Std. Err. z P>|z| [95% Conf. Interval]
————-+—————————————————————
IRS | .0991902 .0354093 2.80 0.005 .0297893 .1685911
M2 | .1713046 .1682697 1.02 0.309 -.1584979 .5011071
SAV | .0909694 .0206885 4.40 0.000 .0504207 .1315181
INF | -.0354344 .0147232 -2.41 0.016 -.0642913 -.0065775
EXP | .0165845 .0114161 1.45 0.146 -.0057905 .0389596
FDI | .0340258 .0211225 1.61 0.107 -.0073735 .0754252
_cons | .2256012 .6265673 0.36 0.719 -1.002448 1.45365
————-+—————————————————————
Appendix 13 – The Hausman Test
—- Coefficients —-
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| re fe Difference S.E.
————-+—————————————————————
IRS | .0991902 .148236 -.0490458 .
M2 | .1713046 .1308447 .0404599 .0281915
SAV | .0909694 .1503282 -.0593588 .
INF | -.0354344 -.0439006 .0084661 .
EXP | .0165845 .0570777 -.0404932 .
FDI | .0340258 .0341773 -.0001514 .
—————————————————————————–
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Appendix 14 – The Autocorrelation Test
Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
F( 1, 39) = 0.599
Prob > F = 0.4438
Appendix 15 – The Heteroscedasticity Test For FEM Regression Model
Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model
H0: sigma(i)^2 = sigma^2 for all i
chi2 (40) = 842.41
Prob>chi2 = 0.000