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This study also proposes a regression model to test the theory in question to obtain robust results. The shortcomings of the regression model used in Devarajan, Swaroop and Zou are discussed in more detail in the relevant section. Devarajan, Swaroop and Zou use an endogenous growth model, in which the household intertemporal utility function, U , equals:. The authors use a production function that has the constant elasticity of substitution property:. Devarajan, Swaroop and Zou find the condition for an increase in the share of g 1 in total public expenditure to have a positive impact on economic growth as in:.

It can be seen that the model does not depend on any initial assumption regarding the productivity of g 1 and g 2. Any component of public expenditure can be productive if its share relative to other components satisfies the condition above. Productivity of public expenditure is not a matter of the sector in which it would be expected to have a positive impact on growth.

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Thus, the productivity of public expenditure in this model is in relative terms, which implies that public expenditure in some sectors that would be considered to contribute to growth may turn out to be detrimental to it if the composition of public expenditure is taken into account. As this paper uses public investment data, in its context of analysis, g 1 and g 2 correspond to the components of public investment. Similarly, for a given budget, if increasing the share of g 1 in g is positively associated with economic growth, then there must be an underinvestment in the first type of public investment.

Thus, the model provides a tool for assessing Turkish public policy regarding the implementation of public investment projects in different sectors and balancing the shares of public investment accordingly for the years between and Devarajan, Swaroop and Zou assume a linear regression model for empirical analysis, and include the shares of each component in total public expenditure and the share of total public expenditure in GDP as explanatory variables in addition to other control variables in their paper. In this paper, too, empirical analysis assumes that the relationship between explanatory variables and the dependent variable is linear.

Post-estimation diagnostics provide evidence that this assumption holds. In which m s represents the other control variables, which are explained at the end of the section. Thus, x 0 is interpreted as the effect of a change in the level of g 1 and g 2. The specification of the regression model becomes slightly more complicated if there are more than two types of public expenditure.

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If there are n types of public expenditure, then the components of public expenditure could be expressed as:. In this case, the regression model could be specified in two ways. In this paper, the regression model is specified as in equation 1 for robustness of results, and simplicity in interpretation. The alternative approach would be to include n — 1 types of public expenditure in the regression model, and to exclude the n th type of public expenditure to avoid perfect collinearity, as in equation 2. However, specifying the regression model as in equation 2 , firstly, complicates the analysis, and, secondly, reduces the reliability of the results.

In this case, including the shares of g 2 , g 3 , It can be seen that specifying the regression model as in equation 2 puts emphasis on the n th type of public expenditure that is left out of the equation. This complicates the analyses as the coefficient of a type of public expenditure depends on the type of public expenditure that is excluded from the model. If, for example, the regression model was specified as in equation 3 , in which the share of g 1 in total public expenditure is excluded, and the share of g n in total public expenditure is included in the model, the values of x 2 , x 3 , Considering there are n types of public expenditure, one would have to choose a regression model among n — 1 versions of equation 2.

This would reduce the robustness of the results because, as the number of types of public expenditure increased, the results between equations would be more volatile, and choosing the appropriate model would be more difficult. In Devarajan, Swaroop and Zou , the regression models are specified as in equation 2.

The authors include the shares of education, health, transportation and communication, and defence in total public expenditure in their regression models. However, they do not explain what type of public expenditure they exclude from the regression models, and, hence, it is actually not possible to interpret the full meaning of the coefficients in their paper.

In this paper, the estimated equation is defined according to equation 1 for robust analyses. Thus, the estimated model in this paper is specified as in equations 4 and 5 :. This paper applies the model in Devarajan, Swaroop and Zou to public investment data. Public investment data used in this paper are taken from the State Planning Organisation now, a section of the Ministry of Development and reflect the amount of public capital expenditure financed by the central government budget. Data used in this paper exclude types of public investment that are made to multiple provinces, as they are not reported in a way that allows one to determine the proportion of public investment received by each province.

The State Planning Organisation disaggregates public investment functionally as energy infrastructure e. Data are deflated for the base year using public investment deflators provided by the DPT For the years between and , they are available in Karaca Both periods of GDP data are provided as deflated series for the base year Karaca, given that the series before and after are calculated differently, adjusts the data for the years between and He does this by assuming that, for any given calculation method with fixed prices, the output shares of provinces should be the same.

Nevertheless, the consistency of the series provided by Karaca , for the years between and , and the Turkish Statistical Institute, for the years between and , are checked, firstly, by calculating GDP growth rate for Turkey for the years between and The annual growth rates calculated from data series used in this paper do not differ from those provided by the World Bank, which is an indication that the GDP series taken from Karaca and the Turkish Statistical Institute are consistent 4.

Data for private capital include gross investments in fixed capital in the manufacturing sector. The data are collected by annual manufacturing sector surveys carried out by the Turkish Statistical Institute. This indicator is included in the regression to capture the impact of private capital on economic growth.

As it measures private investment only in the manufacturing sector, it also reflects the level of industrialisation in the provinces. Data for private capital are deflated for the year using the deflator series for the manufacturing sector in DPT The population growth rate is included in the regressions because it is one of the determinants of the size of the workforce, which has an effect on the denominator of GDP per worker.

The population growth rate is calculated using the census statistics.

Census statistics were collected in , , , and by the Turkish Statistical Institute. The population growth rate reflects the annual growth in the number of people between census years. It must be noted that the data for the population growth rate are problematic by construction as they remain fixed between census years.

Nevertheless, the variable is retained in the regressions for two reasons: firstly, the population growth rate is a key demographic indicator, the exclusion of which could lead to omitted variable bias. Secondly, the Hausman test for model specification in the post-estimation diagnostics suggests using the random-effects and the pooled OLS techniques, both of which render the population growth rate a useful indicator as it changes considerably from province to province due to domestic migration, despite its shortcomings in terms of reflecting the change in population within panels.

In this paper, the economic growth rate is calculated using data for real GDP per worker.

For the denominator, the data for the number of workers are also taken from census data collected in , , , and The number of workers for in-between census years is calculated by assuming the size of the workforce would increase at a fixed annual growth rate. The intervals in census data and the computation of the size of the workforce impose disadvantages on the denominator of GDP per worker similar to those discussed in relation to the population growth rate.

The econometric problem is that if public expenditure were endogenous to the system, ordinary least squares OLS estimates would be biased and inconsistent, because the assumption that the error term and explanatory variables are uncorrelated would be violated. In the literature, there are two common methods to address the problem of simultaneous endogeneity of public expenditure. Some researchers Bose, Haque and Osborn, ; Chamorro-Narvaez, ; Ghosh and Gregoriou, prefer to apply dynamic panel data estimation techniques that are derived from the generalised method of moments GMM , which allows them to use the lagged values of dependent or explanatory variables as instruments.

Others Devarajan, Swaroop and Zou, ; Haque, ; Odedokun, specify the dependent variable as the five-year forward-moving average of per-capita GDP growth rate to address the possibility of reverse causality. Both of these approaches are applicable in the empirical analysis of the relationship between public investment and economic growth.

The advantage of the GMM is that it is a technique developed specifically for the problem of endogeneity. The method introduced by Arellano and Bond has small sample bias; in other words, the technique requires the time dimension of the dataset to be sufficiently large. Later, this weakness was addressed by Arellano and Bover , and Blundell and Bond , and the system GMM estimator was proposed.

However, these techniques require error terms to be uncorrelated between panels Stata, a ; b. Because this paper uses a dataset that consists of provinces and, as the workforce and capital are more fluid between provinces than between countries, the error terms are likely to be correlated between provinces, which violates this assumption 5. Thus, in this paper, to address endogenous simultaneity, the second approach is preferred. It requires calculating the dependent variable as the n -year forwardmoving average of the growth rate.

This introduces serial correlation to standard errors within panels which can be corrected using relevant statistical methods 6. The problem of reverse causality is addressed by avoiding using the contemporaneous values of public expenditure and economic growth rate in the regression. This paper adopts this approach for public investment.

Following the empirical literature Devarajan, Swaroop and Zou, ; Haque, ; Odedokun, , this paper uses the five-year forward-moving average of the growth rate as the dependent variable. However, this paper differs from the cited papers in two aspects. Instead of computing the dependent variable as the nomic growth rate. This is because the geometric average is more reliable than the arithmetic average, as the growth rate is a variable that fluctuates considerably.

Secondly, this paper prefers using data for real GDP per worker instead of real GDP per capita, to account for the changes in the size of the workforce in output production 7. In this paper, the results obtained from the random-effects and pooled OLS techniques are reported.

In panel data analysis, there are two main causes of concern: spatial and temporal dependence. If these lead to dependence between error terms, the inferential statistics become biased.

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If they are common factors that are correlated with the explanatory variables, their omission leads to biased coefficients. To address temporal dependence, the within-estimator that subtracts the individual effects that are fixed over time is used, while, to address spatial dependence, the between-effects estimator that eliminates the individual effects that are constant across the cross-sections space is required. The random-effects estimator is the equally weighted average of the within and between estimators. It allows for spatial dependence between error terms but assumes that it is not a common factor that is correlated with the explanatory variables.

Meanwhile, the pooled OLS estimator assumes the observations are independent. To choose between the econometric techniques, two diagnostic tests are commonly used as indicators. To check whether spatial or temporal dependence is a common factor that is correlated with the explanatory variables, the Hausman test for model specification is applied.

To control for the spatial dependence between error terms, the Breusch and Pagan Lagrangian multiplier test is used. In this paper, the post-estimation diagnostics show that the Hausman test for model specification fails to reject the null hypothesis that there is not a systematic difference between the coefficients produced by the fixed-effects and random-effects techniques, or the fixed-effects and pooled OLS techniques.

This also means that the between-effects and fixed-effects estimators are equivalent, in other words, the results would not differ between the spatial and temporal panel data techniques 8. In the lack of spatial and temporal dependence, the random-effects and pooled OLS techniques are considered more efficient. Thus, in this paper, these techniques are preferred over the fixed-effects or the between-effects technique.

Breusch and Pagan Lagrangian multiplier test indicates spatial dependence in error terms, which leads to serial correlation in residuals between panels and, thus, biased inferential statistics. This requires choosing the random-effects estimator over the pooled OLS estimator because the former is derived from the generalised least squares technique which allows for spatial dependence in error terms. However, this problem can also be addressed by using a correction technique for standard errors that clusters the observations.

Therefore, for the results obtained from the pooled OLS technique, standard errors robust to heteroscedasticity, and serial correlation within panels temporal autocorrelation and between panels spatial autocorrelation are reported, while, for the results estimated by the randomeffects technique, standard errors robust to heteroscedasticity and serial correlation within panels are presented.

As a final note, it must be added that, although the Hausman test for model specification provides evidence regarding the robustness of the coefficients, and despite correcting the standard errors to address the presence of cross-sectional autocorrelation in residuals as indicated by the Breusch and Pagan Lagrangian multiplier test, spatial dependence remains an issue that can affect the robustness of the results in this paper.

Turkey experienced many economic crises between the years and ; thus, on average, the five-year forward-moving geometric average of per-worker real GDP growth rate is low 1. For the same reason, the size of the standard deviation of the dependent variable within panels is rather high.