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Economic Growth, Solow Growth Model, Government Expenditure, Openness.

Since the introduction of the neoclassical model or the Solow-Swan growth model, also known as the exogenous growth model, much attention has been placed on macroeconomic environment and macroeconomic conditions and the role that they play on economic growth. Specifically, variants of this model have been used to assess economic performance (Kormendi and Meguire, 1985; Grier and Tullock, 1989; Barro, 1991, 1997; Fischer, 1993; Easterly and Rebelo, 1993; Barro and Sala-i-Martin, 1995). These studies have surpassed the original use of the Solow-Swan model that focused on productivity growth and the role of savings 1. In the Solow-Swan model, an increase in the saving rate increases the rate of economic growth. Conversely, an increase in the use of capital relative to output reduces growth due to the need of more capital to produce a given level of output.

Utilizing the Solow-Swan framework^{1}, the focus of much of the literature since then has examined a number of economic policies that may affect economic performance, including investments in education and human capital, infrastructure, development and improvement of political and legal institutions, rule of law, level of corruption, level of bureaucracy, and democracy, among others with mixed results from a cross-country prospective. As a result, stable macroeconomic conditions and strong institutional framework are seen as necessary though not sufficient conditions for economic growth (Lewis, 1955; Ayres, 1962; Fischer, 1993; Knack and Keefer, 1995; Mauro, 1995; Hall and Jones, 1999; Rodrik, 1999; Acemoglu et al, 2002). In particular, a stable macroeconomic environment in terms of a targeted low inflation, coherent fiscal policy, responsible budget deficits and appropriate tax policies may favor growth through reduction of uncertainty, whereas macroeconomic instability may have a negative impact on growth through the perception of higher risks and its detrimental effects on productivity and investment. However, there is no broad consensus within the scientific community, as well as politicians, with regard to which policies are more conductive to growth.

However, a key determinant of economic growth stressed and agreed upon is the role of private investment. The relevance assigned to investment triggered by growth has led to an enormous amount of empirical studies examining the relationship between investment and economic growth starting by mid 80s (Kormendi and Meguire, 1985; De Long and Summers, 1991; Levine and Renelt, 1992; Mankiw, 1992; Auerbach et al, 1994; Barro and Sala-i-Martin, 1995; Sala-i-Martin, 1997; Easterly, 1999; Podrecca and Carmeci, 2001). With the rise of globalization and the lessening of trade barriers, another determinant of economic performance receiving attention is openness to trade. Since openness not only facilitates commercial and financial integration, but also the transfer of technology and the diffusion of knowledge from industrialized countries to developing ones. There is a growing empirical literature that has explored this relationship in practice though with inconclusive findings. In fact, there are many researchers who have found that economies which are open to both trade and capital flows exhibit higher GDP per capita and faster growth (Dollar, 1992, Sachs and Warner, 1995, Edwards, 1998, Dollar and Kraay, 2000). However, others researchers have disputed these findings raising concerns about the robustness of these conclusions addressing methodological and measurement problems (Levine and Renelt, 1992; Rodriguez and Rodrik, 1999; Vamvakidis, 2002).

Finally, demographic factors and trends and its impact on economic growth is another relationship that has been attracted interest. In particular, population growth, population density, migration and age distribution, seem to play the major role in economic growth (Kormendi and Meguire, 1985; Dowrick, 1994; Kelley and Schmidt, 1995; Barro, 1997; Bloom and Williamson, 1998; Kelley and Schimdt, 2001). As regards quality of human capital and income distribution, high population growth could have a negative impact on economic growth also affecting investment and saving behavior. On the other hand, population growth may favor the proportion of working-age population with a positive effect on growth, mainly in developing countries. The composition of the population has also important implications for growth. Other related factors such as population density, may be positively linked with economic growth as a result of increased specialization, knowledge diffusion and spillovers. Despite these growing findings, researchers have not found a strong correlation between demographic variables and economic growth (Grier and Tullock, 1989; Pritchett, 2001).

In this paper, we re-examine and extend the Solow-Swan growth model by in several ways to provide additional evidence on the determinants of economic growth. First, we use the most recent available data from the Penn World Table 7.0 (PWT 7.0)^{2}. We use a panel of time series and cross sectional data from 1970 to 2009 covering 155 countries. This is a departure from most studies that utilize a cross-sectional approach or focus on a single country using time series data. Further, all of the data utilized in this paper comes from the PWT 7.0^{3}. Second, we introduce government expenditure and openness into the basic Solow-Swann model. This allows us to test various notions about the role of investment, population, government expenditure, and openness using a fixed effects panel regression. Third, various subsets of the panel including geographic regions, high economic growth countries versus low economic growth countries, and countries with high government expenditure and countries with low government expenditure are analyzed.

In the next section we set out the theoretical model. Data and the statistical models are set forth in section III. Our results indicate that there is an inverse relationship with government expenditure and economic growth and that there is a positive relationship with private investment and economic growth are presented in section IV. We find that how open a country is to international trade may have little impact on economic growth. Our results indicate that government expenditure may have overshot the actual level needed to maintain and/or increase economic growth. We also report that there does appear to be a crowding out effect as there is substitution between private investment and government expenditure and that Increasing private investment on the other hand does lead to increased economic growth. The policy implications and conclusions of these results are finalized in section V.

**a. Review of Endogenous Models and Exogenous Growth Models**

The economic growth theorization started with the neoclassical model or the Solow-Swan growth model, also known as the exogenous growth model. It was an extension of the Harrod-Domar theorization (Harrod, 1942; Domar, 1946) and included a new term, productivity growth. Robert Solow and contemporaneously Trevor Swan developed a relatively simple model, which was later used to fit the data on U.S. economic growth with some success (Solow, 1956; Trevor W. Swan 1956). In this simple model, an increase in the saving rate increases the rate of economic growth. Conversely, an increase in the use of capital relative to output reduces growth due to the need of more capital to produce a given level of output. With all other factors held constant, the output generated by each additional unit of capital will eventually fall, reflecting the law of diminishing returns. An increase of the depreciation rate also reduces growth, because it reduces the amount of saving available for net investment to replace the worn-out or obsolete machinery and equipment. Turning to the issue of conditional convergence, the model predicts convergence in growth rates on the basis that poor economies will grow faster compared to rich countries.

In neoclassical growth models, the long-run rate of growth is exogenous or determined outside the model. A common prediction of these models is that an economy will always converge towards a steady state rate of growth, which depends only on the rate of technological progress and the rate of labor force growth. A country with higher saving rate will experience faster growth. However, in the very long-run capital accumulation appears to be less significant than technological innovation in the Solow model. Nevertheless, technological progress, measured as total factor productivity is determined exogenously in this model. Since the sources of this residual or technological change remain unexplained in the neoclassical economic growth framework, endogenous growth economists believe that improvements in productivity can be linked to a faster pace of innovation and extra investment in human capital.

Is in this avenue where the endogenous growth theory reduces the limitations of the neoclassical growth model by allowing increasing returns to scale through endogenous technological progress linked to human capital accumulation. Even though Arrow and Uzawa pioneered such work in the 1960s (Arrow, 1962; Uzawa, 1965), it was not until the 1990s that diverse ideas have been expressed into formal models in the neoclassical tradition. Endogenous growth economists also stress the need for government and private sector institutions and markets, which nurture innovation and provide incentives for individuals to be inventive. There is also a central role for knowledge as a determinant of economic growth. Triggered by Romer’s (1986) and Lucas’s (1988) seminal work studies within this framework highlighted three significant sources of growth: new knowledge (Romer, 1990; Grossman and Helpman, 1991), innovation (Aghion and Howitt, 1992) and public infrastructure (Barro, 1990). As a result, and in contrast to the neoclassic counterpart, policies are deemed to play a substantial and permanent role in advancing growth on a long run basis. As a result, convergence would not occur under the endogenous growth framework, mainly due to the fact that there are increasing returns to scale.

In order to expand the utility of this framework, additional variables are included as inputs in the production process. The focus in this paper is the inclusion of government expenditure and openness to international trade. Two issues have been investigated with respect to government expenditure on economic growth. The first issue is how the size of government affects economic growth. This issue is analyzed by incorporating the share of government expenditure in gross domestic product (GDP) as input in the production process (see Barro, 1990; Hseih and Lai, 1994; Anaman, 2004 for examples). This is done under the notion that economic growth is best described by an endogenous growth model (Barro, 1990). Anaman (2004) has extended this by adding quadratic and cubic terms of government expenditure to explore the increase in government expenditure over time and its impact on economic growth. Bergh and Henrekson (2011) summarize similar studies and approaches for OECD and EU countries. Wu, et. al. (2010) analyze Granger causality between the size of government and economic growth over the period 1950 to 2004 for 182 countries. The second issue explored is the impact of the growth rate of government expenditure on economic growth as examined by Kormendi and Meguire (1985) and Grier and Tullock (1989). We utilize both types of models in our analysis.

**b. Functional Form**

The key starting point in both exogenous growth and endogenous growth models is the aggregate production for the economy. Usually, a Cobb-Douglas function is set forth as the functional form and additional variables are introduced such as, but not limited to: government expenditure, human capital and net exports. The development and use of this approach is well documented in the literature (see, for example, Mankiw, et. al., 1992; Hseih and Lai, 1995; Barro, 1990; Anaman, 2004). We utilized this approach to examine two issues. The first is the impact of the size of government, as measured in share of government expenditure in GDP, on GDP growth. The model to be estimated follows Anaman (2004):

Where i = 1,….., 155 is the individual country and t = 1971,……, 2009; DY is the annual growth rate of real GDP per capita; INV is the share of investment in GDP; G is the share of government expenditure in GDP; DOPEN is the annual growth rate of openness in GDP (where openness is defined as the share of exports plus imports in GDP); and DPOP is the annual growth rate of population. G^{2} and G^{3} measure the impact economic growth as the size of government changes. Specifically, a small size of government would have a negative impact on economic growth and then as government size increases it would have a positive impact until it grows too large relative to capacity and begins to have a negative impact.

The signs of the coefficients are expected to be: This is based on stylized facts about these parameters (Mankiw et. al., 1992; Anaman, 2004; Weil, 2009).

The second issue we examine is the impact of the growth rate of government expenditure on economic growth. We follow models based on those used by Grier and Tullock (1989) and Kormendi and Meguire (1985). Our specification is

Where i = 1,…..,155 is the individual country and t = 1971,……,2009; DY is the annual growth rate of real GDP per capita; LINV is the natural log of the share of investment in GDP; DG is the annual growth rate of the share of government expenditure in GDP; DOPEN is the annual growth rate of openness in GDP (where openness is defined as the share of exports plus imports in GDP); and DPOP is the annual growth rate of population.

The signs of the coefficients are expected to be: This again is based on stylized facts about these parameters (Mankiw et. al., 1992; Anaman, 2004; Weil, 2009).

As previously stated, all data used in this paper comes from the Penn World Table 7.0. All variables are collected for 1970 to 2009 and after excluding countries with missing data, we constructed a panel of 155 countries with 40 observations each.

Y is the Real GDP per capita is the variable RGDPTT, which is 2005 International dollar per person (2005 International$/Person) Terms of Trade adjusted; INV is ki, Investment Share of PPP Converted GDP Per Capita at 2005 constant prices; G is kg, Government Consumption Share of PPP Converted GDP Per Capita at 2005 constant prices; POP is population in thousands; OPEN is openk, openness is share of GDP Per Capita at 2005 constant prices.^{4}

Basic statistics for each variable are presented in **Table 1**.

*(Insert Table 1 here)*

Variable | Mean | Std. Dev. | Min | Max | Observations | |
---|---|---|---|---|---|---|

Y | overall | 8682.070 | 10482.650 | 142.329 | 89814.010 | N = 6200 |

between | 9757.486 | 225.576 | 45614.930 | n = 155 | ||

within | 3908.513 | -11925.210 | 52881.140 | T = 40 | ||

DY | overall | 0.018 | 0.084 | -1.045 | 0.724 | N = 6045 |

between | 0.018 | -0.045 | 0.106 | n = 155 | ||

within | 0.082 | -1.024 | 0.694 | T = 39 | ||

INV(%) | overall | 23.653 | 11.771 | 0.507 | 90.354 | N = 6200 |

between | 9.067 | 3.940 | 49.535 | n = 155 | ||

within | 7.541 | -18.602 | 83.996 | T = 40 | ||

G(%) | overall | 12.898 | 9.380 | 0.651 | 68.064 | N = 6200 |

between | 8.756 | 2.596 | 55.267 | n = 155 | ||

within | 3.436 | -12.624 | 37.558 | T = 40 | ||

OPEN(%) | overall | 76.179 | 50.413 | 1.035 | 443.175 | N = 6200 |

between | 44.749 | 3.902 | 332.284 | n = 155 | ||

within | 23.486 | -42.048 | 356.537 | T = 40 | ||

POP (thousands) | overall | 31053.450 | 116434.600 | 21.714 | 1323592.000 | N = 6200 |

between | 114966.900 | 42.092 | 1114772.000 | n = 155 | ||

within | 20561.580 | - 263315.200 |
348038.700 | T = 40 |

**Table 1. **Descriptive Statistics

We preformed Levin-Lin-Chu panel unit root tests on the variables and their first differences which are presented in **Table 2**.

*(Insert Table 2 here)*

Variable | Statistic | P-Value |
---|---|---|

LY | -1.629 | 0.052 |

DY | -22.710 | 0.000 |

G | -4.869 | 0.000 |

INV | -7.145 | 0.000 |

OPENK | -2.556 | 0.005 |

POP | -4.490 | 0.000 |

DG | -25.264 | 0.000 |

LINV | -7.419 | 0.000 |

DOPEN | -23.098 | 0.000 |

DPOP | -11.444 | 0.000 |

Note: ADF using 1 lag and including a time trend.

**Table 2. **Levin-Lin-Chu unit-root tests

We included 1 lag for the adjusted Dickey-Fuller (ADF) and a time trend. The null hypothesis is that the panel contains a unit root. For all variables, except for the log of RGDPTT, we reject the null hypothesis of a unit root. Since, the growth rate of RGDPTT is used in this study; we do not consider cointegration given the absence of units in the data^{5}.

**a. Equation 1**

The results of the estimates of Equation 1 are presented in **Table 3**, as Panels A - I.

*(Insert Table 3 Here)*

A. All Countries | B. Latin American Countries | ||||||
---|---|---|---|---|---|---|---|

Estimate | T-Statistic | P-value | Estimate | T-Statistic | P-value | ||

G | -0.0064 | -3.190 | 0.002 | G | -0.022 | -3.090 | 0.0070 |

G2 | 0.0002 | 2.220 | 0.028 | G2 | 0.001 | 2.930 | 0.0090 |

G3 | -0.0000 | -2.050 | 0.042 | G3 | -0.000 | -3.270 | 0.0040 |

DOPEN | -0.0036 | -0.200 | 0.839 | DOPEN | 0.133 | 3.550 | 0.0020 |

INV | 0.0012 | 3.810 | 0.000 | INV | 0.003 | 5.710 | 0.0000 |

DPOP | -0.4630 | -1.750 | 0.081 | DPOP | -0.333 | -1.580 | 0.1330 |

Constant | 0.0504 | 3.480 | 0.001 | Constant | 0.077 | 2.360 | 0.0310 |

R2 | 0.0290 | R2 | 0.118 | ||||

F-Statistic | 3.9100 | F-Statistic | 17.500 | ||||

P-Value | 0.0012 | P-Value | 0.000 | ||||

N | 155 | N | 18 | ||||

C. OECD Countries |
D. African Countries |
||||||

Estimate | T-Statistic | P-value | Estimate | T-Statistic | P-value | ||

G | -0.044 | -3.49 | 0.0020 | G | -0.0061 | -2.170 | 0.036 |

G2 | 0.004 | 2.9 | 0.0080 | G2 | 0.0001 | 0.890 | 0.376 |

G3 | -0.000 | -2.62 | 0.0150 | G3 | -0.0000 | -0.600 | 0.554 |

DOPEN | 0.190 | 5.66 | 0.0000 | DOPEN | -0.0367 | -1.470 | 0.148 |

INV | 0.003 | 5.09 | 0.0000 | INV | 0.0019 | 2.590 | 0.013 |

DPOP | -1.167 | -3.17 | 0.0040 | DPOP | -0.4704 | -1.230 | 0.225 |

Constant | 0.143 | 3.41 | 0.0020 | Constant | 0.0436 | 1.900 | 0.064 |

R2 | 0.2080 | R2 | 0.0578 | ||||

F-Statistic | 21.540 | F-Statistic | 5.4100 | ||||

P-Value | 0.000 | P-Value | 0.0000 | ||||

N | 24 | N | 44 |

** E. Asian Countries**

Estimate | T-Statistic | P-value | |
---|---|---|---|

G | 0.010 | 0.800 | 0.435 |

G2 | -0.001 | -0.970 | 0.347 |

G3 | 0.000 | 1.230 | 0.235 |

DOPEN | 0.012 | 0.290 | 0.772 |

INV | 0.001 | 4.490 | 0 |

DPOP | 0.406 | 1.070 | 0.298 |

Constant | -0.049 | -0.910 | 0.376 |

R2 | 0.039 | ||

F-Statistic | 14.960 | ||

P-Value | 0.000 | ||

N | 19 |

F. Countries with High Economic Growth | G. Countries with Low Economic Growth | ||||||
---|---|---|---|---|---|---|---|

Estimate | T-Statistic | P-value | Estimate | T-Statistic | P-value | ||

G | -0.013 | -3.080 | 0.003 | G | -0.0041 | -2.150 | 0.035 |

G2 | 0.000 | 2.550 | 0.013 | G2 | 0.0001 | 1.330 | 0.186 |

G3 | -0.000 | -2.350 | 0.021 | G3 | -0.0000 | -1.290 | 0.202 |

DOPEN | 0.008 | 0.400 | 0.451 | DOPEN | -0.0106 | -0.420 | 0.672 |

INV | 0.001 | 2.750 | 0.008 | INV | 0.0009 | 3.220 | 0.002 |

DPOP | -0.719 | -3.150 | 0.002 | DPOP | -0.4105 | -1.260 | -1.260 |

Constant | 0.093 | 3.560 | 0.001 | Constant | 0.0302 | 1.900 | 0.061 |

R2 | 0.054 | R2 | 0.019 | ||||

F-Statistic | 3.250 | F-Statistic | 4.360 | ||||

P-Value | 0.007 | P-Value | 0.001 | ||||

N | 75 | N | 80 |

H. Countries with High Government Size | I. Countries with Low Government Size | ||||||
---|---|---|---|---|---|---|---|

Estimate | T-Statistic | P-value | Estimate | T-Statistic | P-value | ||

G | -0.008 | -1.910 | 0.060 | G | 0.000 | 0.020 | 0.986 |

G2 | 0.000 | 1.490 | 0.141 | G2 | -0.001 | -0.770 | 0.442 |

G3 | -0.000 | -1.440 | 0.155 | G3 | -0.000 | 1.510 | 0.136 |

DOPEN | -0.020 | -0.810 | 0.419 | DOPEN | 0.024 | 0.910 | 0.368 |

INV | 0.001 | 2.110 | 0.038 | INV | 0.001 | 4.720 | 0.000 |

DPOP | -0.649 | -2.860 | 0.006 | DPOP | -0.018 | -0.030 | 0.973 |

Constant | 0.090 | 2.780 | 0.007 | Constant | 0.010 | 0.260 | 0.793 |

R2 | 0.046 | R2 | 0.034 | ||||

F-Statistic | 4.790 | F-Statistic | 14.220 | ||||

P-Value | 0.000 | P-Value | 0.000 | ||||

N | 70 | N | 85 |

**Table 3. Estimates of Equation 1: Government Size on Economic Growth**

We used Stata 12.0 SE edition to estimate cross-sectional time series regressions with fixed effects and robust errors. Panel A contains the results for all countries^{6}. Panels B through I contain the results for subsets of the countries based on regional location, economic standing, rate of economic growth and government size. The all country results in Panel conform to the theoretical model set forth as equation 1. All variables have the expected sign and are a significant at the 5% level for a one-tailed hypothesis test, except for the growth of openness which has the correct sign, but is not significant. We find that an increase in the size of government has a negative impact on economic growth. Further, the quadratic term on government size indicates that this negative impact occurs at an increasing rate. The significant cubic term reveals that as government size grows even larger this negative impact on economic growth is even more detrimental.

These findings are consistent with Anaman (2004) for Brunei and Bergh and Henrekson (2011) for OECD/EU countries. The signs of both private investment (positive) and population growth (negative) are consistent with the theory of the Solow model. This indicates the importance of promoting private savings for economic growth as well as reducing the population growth as a means of increasing economic growth.

Panels B through J highlight the differences that emerge among select groups of countries. Panels B and C set forth the results for Latin American and OECD countries. For both these sets of countries all variables have the expected signs and are the coefficients are significant at the 5% (for population growth for Latin America 10%). Openness to trade is positive and significant for these two groups, respectively. The results for government size are similar as for the all country results.

From **table 3**, the adjusted elasticity of the government size for Latin American countries is 12% while 17% for OECD countries. If we compared these estimated elasticities with current values of government sizes for the 2009-2010 period (40% and 34% for the two regions, respectively), we can infer that the actual size of government is an important factor may hamper economic growth in both regions; directly for the OECD countries and indirectly due to openness to trade in Latin American countries. Nevertheless, the current debt and financial crisis of developed countries has triggered fiscal stimulus in order to prevent deeper economic downturns.

As indicated in Panels D and E, the results do not support the use of a cubic function to describe the relationship government size and economic growth. The quadratic and cubic terms for government size are not significant. For Africa (Panel D) only government size and private investment are significant, while for Asia (Panel E) only private investment is significant.

We then divided the countries into 2 groups, those with economic growth rates above the average and those with economic growth rates below the average (results in Panels F and G). As can be seen in Panel F, countries with above average economic growth confirm to the all country results in terms of expected signs and significance. Growth of openness is still insignificant. Those countries with below average economic growth rates have only 2 variables significant, government size and private investment.

We also divided the countries into groups based on government size; A group with government above the overall mean of government size (Panel H) and a group with government size below the overall mean of government size (Panel I). Panel H, which contains the countries above the mean government size, reveals that the results for these countries follow the exact same pattern as those from those countries with above average economic growth rate. That is, these countries conform to the theory set on government size and economic growth as well as the predictions of the Solow growth model. The results for those countries with below average size of government show that only private investment has the correct sign (positive) and is significant. For these countries, economic growth is not coupled to the size of government and relies more on the role of the private sector in promoting economic growth.

**a. Equation 2**

The results of the estimates of Equation 2 are presented in **Table 4**, Panels A-I.

*(Insert Table 4 here)*

A. All Countries | B. Latin American Countries | ||||||
---|---|---|---|---|---|---|---|

Estimate | T-Statistic | P-value | Estimate | T-Statistic | P-value | ||

LINV | 0.028 | 3.480 | 0.001 | LINV | 0.052 | 5.910 | 0.000 |

DG | -0.061 | -3.370 | 0.001 | DG | -0.120 | -2.210 | 0.041 |

DOPEN | -0.003 | -0.160 | 0.872 | DOPEN | 0.122 | 3.600 | 0.002 |

DPOP | -0.444 | -1.690 | 0.094 | DPOP | -0.449 | -2.020 | 0.059 |

Constant | -0.059 | -2.500 | 0.013 | Constant | -0.127 | -4.980 | 0.000 |

R2 | 0.030 | R2 | 0.121 | ||||

F-Statistic | 9.710 | F-Statistic | 10.950 | ||||

P-Value | 0.000 | P-Value | 0.000 | ||||

N | 155 | N | 18 |

C. OECD Countries | D. African Countries | ||||||
---|---|---|---|---|---|---|---|

Estimate | T-Statistic | P-value | Estimate | T-Statistic | P-value | ||

LINV | 0.059 | 6.630 | 0.000 | LINV | 0.038 | 2.580 | 0.013 |

DG | -0.446 | -3.900 | 0.001 | DG | -0.052 | -3.180 | 0.003 |

DOPEN | 0.088 | 3.000 | 0.006 | DOPEN | -0.034 | -1.340 | 0.186 |

DPOP | -0.457 | -1.750 | 0.093 | DPOP | -0.470 | -1.250 | 0.219 |

Constant | -0.160 | -5.790 | 0.000 | Constant | -0.089 | -2.190 | 0.034 |

R2 | 0.405 | R2 | 0.047 | ||||

F-Statistic | 51.270 | F-Statistic | 8.580 | ||||

P-Value | 0.000 | P-Value | 0.000 | ||||

N | 24 | N | 44 |

E. Asian Countries | |||
---|---|---|---|

Estimate | T-Statistic | P-value | |

LINV | 0.030 | 3.710 | 0.002 |

DG | -0.027 | -0.350 | 0.731 |

DOPEN | -0.001 | -0.020 | 0.988 |

DPOP | 0.430 | 1.130 | 0.272 |

Constant | -0.068 | -2.300 | 0.034 |

R2 | 0.032 | ||

F-Statistic | 7.470 | ||

P-Value | 0.001 | ||

N | 19 |

F. Countries with High Economic Growth | G. Countries with Low Economic Growth | ||||||
---|---|---|---|---|---|---|---|

Estimate | T-Statistic | P-value | Estimate | T-Statistic | P-value | ||

LINV | 0.024 | 1.840 | 0.071 | LINV | 0.032 | 4.310 | 0.000 |

DG | -0.023 | -0.800 | 0.427 | DG | -0.098 | -4.360 | 0.000 |

DOPEN | -0.019 | -0.760 | 0.451 | DOPEN | 0.032 | 1.460 | 0.148 |

DPOP | -0.638 | -2.800 | 0.007 | DPOP | -0.019 | -0.040 | 0.970 |

Constant | -0.043 | -1.120 | 0.267 | Constant | -0.079 | -3.920 | 0.000 |

R2 | 0.033 | R2 | 0.045 | ||||

F-Statistic | 4.400 | F-Statistic | 13.680 | ||||

P-Value | 0.003 | P-Value | 0.000 | ||||

N | 75 | N | 80 |

H. Countries with High Government Size | I. Countries with Low Government Size | ||||||
---|---|---|---|---|---|---|---|

Estimate | T-Statistic | P-value | Estimate | T-Statistic | P-value | ||

LINV | 0.048 | 3.000 | 0.004 | LINV | 0.018 | 2.750 | 0.007 |

DG | -0.048 | -1.210 | 0.231 | DG | -0.064 | -3.210 | 0.002 |

DOPEN | 0.006 | 0.320 | 0.751 | DOPEN | -0.007 | -0.280 | 0.783 |

DPOP | -0.738 | -3.160 | 0.002 | DPOP | -0.393 | -1.200 | 0.233 |

Constant | -0.112 | -2.310 | 0.024 | Constant | -0.037 | -1.960 | 0.054 |

R2 | 0.049 | R2 | 0.025 | ||||

F-Statistic | 4.290 | F-Statistic | 8.100 | ||||

P-Value | 0.004 | P-Value | 0.000 | ||||

N | 70 | N | 85 |

**Table 4. **Estimates of Equation 2: Growth of Government on Economic Growth

Again, we used Stata 12.0 SE edition to estimate cross-sectional time series regressions with fixed effects and robust errors. Panel A contains the results for all countries. Again, Panels B through I contain the results for subsets of the countries based on regional location, economic standing, rate of economic growth and government size. The all country results in Panel A conform to the theoretical model set forth as equation 2. The results are very similar to those of Equation 1. All variables have the expected sign and are a significant at the 5% level for a one-tailed hypothesis test, except for openness to trade which has the correct sign, but is not significant. We find that an increase in the growth of government has a negative impact on economic growth. This finding confirms to those of Grier and Tullock (1989) and Kormendi and Meguire (1985). The signs of both private investment (positive) and population growth (negative) are again consistent with the theory of the Solow model. However, our results differ from Wu, et.al. (2010) who test for Granger causality and find that for a panel of 182 countries from 1950 to 2004, growth of government expenditure Granger causes economic growth with a positive effect. We re-estimated our panel up to 2005, but our results were unchanged. The findings of Wu, et. al. are interesting given that fixed effect panel regressions have consistently found an inverse relationship between government size and growth as we do in this paper.^{7}

Panels B through J highlight the differences that emerge among select groups of countries. Panels B and C set forth the results for Latin American and OECD countries, respectively. For both these sets of countries all variables have the expected signs and are the coefficients are significant at the 5% level for a one-tail t-test. Openness to trade is positive and significant for these two groups, respectively.

As indicated in **Table 4** Panels D, the results for Africa do support that growth of government has a negative impact on economic growth. On the other hand, **Table 4** Panel E is similar for what was found in **Table 3**, Panel E for Asia, where growth of government is not related to economic growth.

We again divided the countries into 2 groups, those with economic growth rates above the average and those with economic growth rates below the average (results in Panels F and G). As can be seen in Panel F, countries with above average economic growth are influenced by increasing private investment and lowering of population growth. Country’s openness is still insignificant. Those countries with below average economic growth rates conversely are have their economic growth raised by increasing private investment, but have been hurt by the negative relationship between growth of government and economic growth.

We also divided the countries into groups based on government size, a group with government size above the overall mean of government size (Panel H) and a group with government size below the overall mean of government size (Panel I). Panel H, which contains the countries above the mean government size, reveals that the government growth has no impact on economic growth for those countries with above average economic growth rate. The results for those countries with below average size of government show that private investment has the correct sign (positive) and is significant and that increasing government growth has a negative relationship with economic growth. Growth of government expenditure (making government larger) would only reduce economic growth for these countries. This suggests that this countries maybe experiencing inefficiencies in using government expenditure to fuel future growth.

**V. Empirical Results**

Our purpose was to analyze the PWT 7.0 data to see what insights could be gleaned about government expenditure and economic growth. We confined our empirical analysis to only the PWT 7.0 data. We used two different modifications of the Solow growth model to examine the effect of the size of government on economic growth and the growth of government expenditure on economic growth. We applied this model to 155 countries over a 40 year period.

The basic precepts of the Solow model were found to hold in both cases analyzed. Investment has a positive effect on economic growth while population growth has a negative effect on economic growth. In the first model, we applied a cubic function to the size of government (as measured by share of GDP) and incorporated that into the Solow growth model. We found that as the size of government increases economic growth decreases at an increasing rate. We also included a measure of openness of the economy, but it was found not to be significant. Similar results were found in the second model. Growth of government expenditure had a negative effect on economic growth.

We applied each model to countries based on regional location, size of government and economic growth. The results were noticeably different based on this disaggregation. The best fit of each model was found for the OECD countries and Latin American countries, respectively. Openness was found to be positive and significant for them. Economic growth in African countries was mostly impacted by the size and growth of government as well as private investment. Economic growth in Asian countries was only influenced by investment. Countries with above economic growth while effected by the size of government were not impacted by the growth of government.

The role of private investment as well as reductions in population growth to increase economic growth should continue to guide policy makers in all countries on what factors to focus on to enhance economic growth. From the results of this paper, that would be private savings for investment and reducing the population growth rate.

Our results indicate that both the size of government and growth of government expenditure have important and significant effects on economic growth. In all cases, countries can benefit by a reduction in the size and growth of government expenditure. This finding suggests that inefficiencies exist in the public sector as a means to increase economic growth. Governments have not only bailed out many of the bad assets from private institutions but due to the recession face continuing heavy borrowing.

Slow growth in the real economy and high unemployment will retard tax revenues while require higher government spending such as on unemployment benefits and job creation activities. When fiscal crises occur during recessions, as they often do, such policy changes can exacerbate the economic downturns, though, some studies suggest that certain types of fiscal austerity may stimulate economic growth^{8}. Perhaps good data, such as the one provided by the Penn World Table, will tell us about these outcomes in a near future.

^{1}Robert Solow and contemporaneously Trevor Swan developed a relatively simple model, which was later used to fit the data on U.S. economic growth with some success (Solow, 1956; Trevor W. Swan 1956).

^{2}Alan Heston, Robert Summers and Bettina Aten, Penn World Table Version 7.0, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania, May 2011.

^{3}Note on use of PWT data versus other data like World Bank.

^{4}Data used in this study available from the authors by request.

^{5}We used Stata SE version 12.0 for all calculations in this paper.

^{6}We also estimated equation 1 excluding the slow growing oil exporting countries. There were only 3 that made our sample and dropping them did not change our findings.

^{7}One reason may be that our empirical model is different than the one used by Wu, et.al. Further, Hsieh and Lai (1995), report results that are ambiguous with respect to government expenditure and economic growth for the OECD countries.

^{8}See, for example, Alberto Alesina, 2010. ”Fiscal Adjustments: Lessons from Recent History” (paper presented at a meeting of Ecofin, Madrid, April 15, 2010); and Alberto Alesina and Silvia Ardagna, 2009. Large Changes in Fiscal Policy: Taxes versus Spending, Working Paper No. 15438 (Cambridge, Mass.: National Bureau of Economic Research, October.)

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