Economic growth: an extension of the augmented Solow growth model : empirical analysis of 22 OECD countries

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Economic growth: an extension of the

augmented Solow growth model.

Empirical analysis of 22 OECD countries.

ABSTRACT

This thesis examines whether the augmented Solow growth model (see Mankiw et al. (1992)) still holds in the period 1984-2014 for 22 OECD countries. Furthermore, it examines whether the

model improves by including additional relevant variables. The additional variables are government expenditure, inflation, government debt, openness to trade and the undervaluation of

the exchange rate. The research shows that there is no clear evidence that the augmented Solow growth model holds. The variables human capital and population growth show insignificant results. However, the additional variables do improve the explanatory power of the model. The R-squared within goes up from 0.5308 for the augmented Solow growth model to 0.5742 for the

extended augmented Solow growth model.

Name: Kelsey Daniëlsson Student number: 10547150 Study: Economics and business Field: Economics and Finance

Subject: Bachelor thesis and thesis seminar: Economics and Finance Thesis Supervisor: Rutger Teulings

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Chapter 1: introduction

Many countries find economic growth important, since it helps people shift to a higher indifference curve. It reduces unemployment and determines a household’s purchasing power. Solow (1956) is one of the first researchers that developed a model predicting long-run economic growth. In 1987, the researcher received the Nobel Prize in Economics for his work on the Solow growth model. According to this model, the savings rate and the population growth rate are the key determinants of economic growth. A high savings rate leads to economic growth and a high population growth rate leads to an economic loss.

However, 36 years later, the researchers Mankiw, Romer & Weil (1992) tested the empirics of Solow’s theoretical model and show that it does not fully explain cross-country income growth differences. That is why the researchers add an additional variable to Solow’s model: human capital. This addition improves the model’s predictive power from 50% to 80%. To distinguish this alternation of the model from the original model, it is identified as the augmented Solow growth model.

Both models are based on data from 1960 to 1985. Due to the changing world’s

economy, it is uncertain whether the augmented Solow growth model is still able to explain the 80% cross-country income growth differences.

Therefore, with the use of a dynamic panel data approach, the aim of this thesis is to see if the results of the augmented Solow growth model still hold in the period 1984-2014 for 22 OECD countries. Appendix A of this research provides a list of the participating countries in this paper. Furthermore, this paper examines whether an extension of the model leads to a better explanation of economic growth. Whereby, additional variables are added to the model. These additional variables are inflation, government expenditure, government debt, undervaluation of the exchange rate and openness to trade.

The results of this research show that there is no clear evidence that the augmented Solow growth model holds. The variables human capital and population growth show insignificant results. However, the inclusion of the extra variables does improve the explanatory power of the model.

This paper is structured as follows. First, chapter 2 covers an illustrative framework of the augmented Solow growth model and the extra variables. Secondly, chapter 3 describes the

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methodology of this research paper. Chapter 4 shows the empirical results of the model and the extra variables. Thereafter, chapter 5 gives a sensitivity analysis of the relevant data. Finally, chapter 6 draws a conclusion from the findings of this research.

Chapter 2: an illustrative framework

Section 2.1 contains a theoretical background on the (augmented) Solow growth model. Section 2.2 describes the interest of adding additional variables to the augmented Solow growth model.

2.1 The (augmented) Solow growth model

Solow (1956) concludes that economic growth is based on the level of savings and

population growth. The researcher shows that a high savings rate leads to economic growth and a high population growth rate leads to an economic loss.

The Solow growth model starts with a standard neoclassical production function, with a decreasing return to capital. This means that the marginal product of capital is positive, but declines when capital increases (Romer, 2012, p. 12). The two inputs of the model are capital and labor, paid by their marginal products. The Solow growth model takes the population growth rate, technological progress and the savings rate as exogenous.

𝑌 𝑡 = 𝐾 𝑡 ! _{𝐴 𝑡 𝐿 𝑡} !!!_, _{0 < 𝛼 < 1. (1)}

The classical Cobb-Douglas function (Equation (1)) focuses on four variables: output (Y), capital (K), labor (L), and technology level (A). 𝐴 𝑡 and 𝐿 𝑡 enter the equation multiplicatively, which is referred as the effective labor (Mankiw, Romer & Weil, 1992, p. 409). Labor and the technological level grows at ! !

! ! = n and ! !

!(!) = g. Where 𝐿 𝑡 and 𝐾(𝑡) stand for the variable’s derivative with respect to time. It is the shorthand for!" !

!" and !" !

!" (Romer, 2012, p. 13). The model takes a closed economy as an assumption. This makes the total savings of a country equal to their total investments (Westerhout, 2016). That is why an exogenous constant fraction of output, s, is invested. Whereby s refers as the savings rate. One unit output that is devoted to

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investment produces one new unit of capital. In addition, existing capital depreciates at rate δ. This leads to the following equation:

𝐾 = 𝑠𝑌 𝑡 − 𝛿𝐾 𝑡 (2)

Next to the closed economy, the model is based on a few other simplifying assumptions. First, there is no government interference. Secondly, it ignores employment fluctuations. Furthermore, it produces only one single good, which is sold in a perfectly competitive market (Romer, 2012, p. 14).

One of the advantages of a Cobb-Douglas function is that it is homogeneous of degree one. Accordingly, it can transform to its intensive form. For this reason, equation (1) is divided by 𝐴 𝑡 𝐿(𝑡), and looks as follow:

Y t A t L(t)=

K t ! _{A t L t} !!!

A t L(t) → = 𝑦(𝑡) = 𝑓 𝑘(𝑡) (3) The 𝑦(𝑡), in other form, ! !

! ! !(!) shows the output per effective unit of labor. The 𝑘 𝑡 as in, ! !

! ! ! ! represents the amount of capital per effective unit of labor. This shows that 𝑦(𝑡) =

𝑘 𝑡 !_{. After this, the first derivative of 𝑘(𝑡), with respect to time, shows the following results:}

𝑘 𝑡 = 1 𝐴 𝑡 𝐿 𝑡 𝐾 𝑡 − 𝐾 𝑡 𝐿 𝑡 (𝐴 𝑡 𝐿 𝑡 )!𝐴 𝑡 − 𝐾 𝑡 𝐴 𝑡 𝐴 𝑡 𝐿 𝑡 !𝐿 𝑡 (4)

After rearranging the variables and substituting the growth rates into equation (4), the following equation will appear:

𝑘 𝑡 = 𝑠𝑦 𝑡 − 𝑛 + 𝑔 + 𝛿 𝑘 𝑡 → = 𝑠𝑘 𝑡 ∝_{− 𝑛 + 𝑔 + 𝛿 𝑘 𝑡 (5)}

Equation (5) shows that 𝑘 converges to a steady state, defined by:

𝑘∗ ₌ 𝑠

𝑛 + 𝑔 + 𝛿

! !!∝

(6)

Equation (6) shows Solow’s (1956) findings, mentioned in the introduction. Economic growth is based on the savings rate and the population growth rate. It shows that the savings rate is

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population growth rate is negatively correlated with the steady state of capital. When n goes up,

k* goes down. Substituting equation (6) into equation (1), andtransformit to its natural

logarithm results in the subsequent equation:

ln ! ! ! ! = ln 𝐴 0 + 𝑔𝑡 + ∝ !!∝ ln 𝑠 − ∝ !!∝ ln 𝑛 + 𝑔 + 𝛿 (7) 𝐿𝑛 𝐴 0 = 𝛼 + 𝜖, captures not only technology but resource endowments, climate, and institutions as well (Mankiw, Romer & Weil, 1992, p. 411). Solow (1956) assumes that g and δ are constant across countries. This means that the advancement of knowledge is not country-specific. The researcher applies a value of 0.02 for g and 0.03 for δ. Except for technological change, it is assumed that all variables are unaffected by the error term.

As mentioned in the introduction of this research, the theoretical framework of Solow does not give a good explanation for the cross-income growth differences. Mankiw, Romer and Weil (1992) examinethe theoretical model of Solow, empirically, and conclude that the findings of Solow are overstated. The empirics show that the impacts of savings and labor force growth are smaller than Solow’s findings.That is why the researchers add an additional variable to the Solow growth model: human capital. To distinguish this alternation of the model from the original model, it is identified as the augmented Solow growth model. The allocation of the resources to human-capital accumulation is exogenously determined. It is a fraction of the total amount of savings, 𝑠_! invested in human capital. The remaining part is invested in capital,𝑠_!. One unit output that is devoted to investment in human capital produces one new unit of human capital. One unit output that is devoted to investment in capital produces one new unit of capital. In addition, existing human capital and capital both depreciate at rate δ. This leads to the

following two equations:

𝐻(𝑡) = 𝑠_!𝑌 𝑡 − 𝛿𝐻 𝑡 8 𝐾 𝑡 = 𝑠_!𝑌 𝑡 − 𝛿𝐾 𝑡 (9)

Both fractions are positively correlated with the steady state of capital and the steady state of human capital. The augmented Solow growth model is based on a Cobb Douglas function, just as the Solow growth model.

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𝑌 𝑡 = 𝐾 𝑡 𝐻 𝑡 ! _{𝐴 𝑡 𝐿 𝑡} !!!!!₍₁₀₎

The mathematics of the augmented Solow growth model are the same as mentioned above. Following the same steps as mentioned above, will equation (10) eventually convert into the subsequent equation: 𝐿𝑛 𝑌 𝑡 𝐿 𝑡 = ln 𝐴 0 + 𝑔𝑡 + α 1 − α − βln 𝑠! − α + β 1 − α − βln 𝑛 + 𝑔 + δ + β 1 − α − βln 𝑠! (11) By adding human capital to the Solow growth model, the model better clarifies the

differences of countries among growth. Statistically, Mankiw, Romer & Weil (1992) show that the augmented Solow growth model clarifies roughly 80% of the cross-country variation in

income. While the Solow growth model clarifies 50% of the cross-country variation in income. In the extension of this, Barro and Sala-i-Martin (1992) indicate that low-income countries can

only converge into high-income countries if they have a high level of human capital per person.

2.2 Additional variables of interest Inflation

According to Fisher (1993), capital accumulation and productivity growth have a negative association with inflation. In other words, inflation has a negative correlation with economic growth. Inflation is an indicator whether the government is able to get a grip on the overall management of the economy. For example, in the case of hyperinflation, which is an inflation of 50% per month or more. It indicates that the government lost grip on controlling the economy of the country. Equivalently, they lost the control of influence on the economy, whichcreates an unsustainable macroeconomic framework. This creates uncertainty, which has two underlying reasons. First, it reduces the efficiency of the price mechanism, as prices greatly fluctuate. Secondly, it reduces the rate of investment. Investors will wait to invest, before committing themselves to certain projects (Fischer, 1993, pp. 488-502).

Barro (1995) shows that a 10 % increase of average inflation reduces the growth rate of GDP per capita by 0.2-0.3 %. At the same time, it decreases the investment to GDP ratio by

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0.6%. The variance of inflation is an important factor as well. A high variability of inflation goes with a high average of inflation (Okun, 1975, p. 497).

Government consumption

In addition to inflation, is government consumption also an important variable. According to Barro (1991), has real government consumption expenditure to GDP ratio a negative association with economic growth and investment. The reason for this negative association is that

government consumption has no direct effect on private productivity. It reduces savings and growth by the distorting effects of taxation and government expenditure programs. In addition, in the paper “The macroeconomic effects of government debt in a stochastic growth model”

published in 1996, states that the impact of government expenditure depends on how it is financed. Ludvigson (1996) shows that distortionary tax finance can lead to a decline in output, consumptions, and investments. For example, a tariff on imported products is a distortionary tax. It makes the imported products more expensive and incentives the consumer to buy domestic products. However, for an economy where most of the government debt is held in the country is own currency, deficit finance of government expenditure can increase output and consumption.

Mankiw (2013) has another perspective on the contribution of government expenditure to

economic growth than Barro (1992) and Ludvigson (1996) have. Mankiw (2013) concludes that a 1 euro increase in government expenditure leads to an increase in income greater than 1 euro. His theory is based on the government-purchases multiplier, which is derived from the

Keynesian cross model. The mechanism of this model shows that expenditure raises income and consumption. Thereafter, consumption further raises income, which raises consumption again, and so on.

Government debt

Additionally, during the financial crisis in 2008, many governments increased their debt. In order to save different financial institutions from going bankrupt, several governments gave financial aid to those institutions. In the EMU alone, the gross government debt to GDP ratio increased from 66%, in 2007 to 85%, in 2010 (Checherita-Westphal & Rother, 2012, p. 1393). Checherita-Westphal & Rother (2012) show that a consequence for this is the concave effect on

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government growth. Despite, this negative non-linear effect, it only influences growth after a certain threshold. It affects the economic growth rate, only if the debt to GDP ratio is at least 90-100%. For the 95% confidence interval, this effect starts at 70-80%. Nonetheless, the model that Chechererita-Westphal & Rother (2012) use may deal with a potential edogeneity problem. In addition to the causal link from the independent variable to the dependent variable, there is a possible causal link from the dependent variable to the independent variable. This is known as reverse causality.

Openness to trade

Another important variable to take into account is the openness to trade. Obviously, export has a positive correlation with economic growth (Feder, 1982, p. 59.) However, many scientists focus too much on export, instead of export and import together. Yanikkaya (2002) stated that countries with a high trade share are likely to grow faster than countries with a low trade share. Statistically, a 10 % increase in trade volume increases the average GDP per capita by 0.18%, annually.

Undervaluation of the exchange rate

The last important variable is the over-, and undervaluation of the real exchange rate, compared to the absolute purchase power parity. The nominal exchange rate represents how much of one currency can be traded for a unit of another currency. The real exchange rate is the nominal exchange rate times the relative prices of two countries. The absolute purchase power parity shows the price of a fixed bundle of goods in one country, compared to the price of the same bundle of goods in another country (Pilbeam, 2013, pp. 10-126). The real exchange rate is undervalued when it is lower than the absolute purchase power parity. Rodrik (2008) concludes that the undervaluation of the real exchange rate a positive effect has on economic growth. This means that the overvaluation of the real exchange rate an adverse effect has on economic growth. The reason for this is that it links back to macroeconomic stability. An overvalued currency encourages spending on imported products and depresses the demand for export products. It creates an unsustainably large current account deficit. Thereafter, it is associated with foreign currency shortages. It means that the demand for a foreign currency is higher than its supply. In this case, if a country has a high amount of debt in another currency than their own, eventually they will be unable to pay back their debt.

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Chapter 3: methodology

Chapter 3 explains the structure of the empirical model of this thesis. Section 3.1 describes the empirical models. Section 3.2 gives an overview of the relevant data. Section 3.3 contains a synopsis of the theory of panel regressions.

3.1 The empirical model

The relevant factors contributing to economic growth, discussed in chapter 2 of this research, are all included in the empirical model of this research. The empirical model of this research bases on equation (9) of this research:

𝐿𝑛 𝑌 𝑡 𝐿 𝑡 = ln 𝐴 0 + 𝑔𝑡 + α 1 − αln 𝑠! − α 1 − αln 𝑛 + 𝑔 + δ + β 1 − αln 𝑠! (11) To this extent, using the Ordinary Leas Square (OLS) method, the following 2 panel regressions are analyzed.

• Regression 1: The augmented Solow growth regression

GROWTH_!" = β_!+ β_!ln (GDPpc)_!,!!!+ β_!ln 𝑤𝐺𝐷𝑃𝑝𝑐 _!"+ β_!ln 𝑤𝐺𝐷𝑃𝑝𝑐 _!.!!! + β_!ln (INVEST)_!"+ β_!ln (∆NGO)_!"+ β_!ln (SCHOOL)_!"+ α_! + ε_!" (𝟏)

This research examines whether the augmented Solow growth model still holds in the period 1984-2014 for 22 OECD countries. First, the growth rate of equation (11) should be determined. Therefore, the first difference of the dependent variable of equation (11) is measured as ln GDPpc _!,!− ln (𝐺𝐷𝑃𝑝𝑐)_!,!!!. 𝐺𝑅𝑂𝑊𝑇𝐻_!" represents ln GDPpc _!,! − ln (𝐺𝐷𝑃𝑝𝑐)_!,!!!. It indicates as the first difference of the logarithm GDP per capita. The independent variable, ln (GDPpc)!,!!!, is a lagged variable and represents the initial value of the GDP per capita. By

subtracting ln (GDPpc)!,!!!from the left side of the regression equation, and adding the same

variable to the right side of the regression equation, the growth rate of GDP per capita can be measured (Stock & Watson, 2015, pp. 570-574). ln 𝑤𝐺𝐷𝑃𝑝𝑐 !" and ln 𝑤𝐺𝐷𝑃𝑝𝑐 !.!!!

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between the GDP per capita of the 22 countries of this sample and the countries outside this sample. The variable ln (𝐼𝑁𝑉𝐸𝑆𝑇)!" represents ln 𝑠! in equation (11). It is the fraction of

domestic investment devoted to capital. ln 𝑁𝐺𝑂 _!" represents ln 𝑛 + 𝑔 + 𝛿 in equation (11). Just as in equation (11), are population growth, technological change and depreciation rate summed as one variable. However, to correct for a unit-root in the variable ln (𝛥𝑁𝐺𝑂)_!" replaces, ln (𝑁𝐺𝑂)!", which is the first difference of ln (𝑁𝐺𝑂)!". ln 𝑆𝐶𝐻𝑂𝑂𝐿 !! represents

ln 𝑠_! in equation (11). It is the fraction of domestic investment devoted to human capital. Regression 1 is a fixed effect regression. Therefore, α_!, shows the country-specific variation that is constant across time.

• Regression 2: The extended augmented Solow growth regression

𝐺𝑅𝑂𝑊𝑇𝐻_!" = β_!+ β_!ln (GDPpc)_!,!!!+ 𝛽_!ln 𝑤𝐺𝐷𝑃𝑝𝑐 _!"+ 𝛽_!ln 𝑤𝐺𝐷𝑃𝑝𝑐 _!.!!!+ β_!ln (INVEST)_!"+ β_!ln (∆NGO)_!"+ β_!ln (SCHOOL)_!"+ β_!𝐺𝑂𝑉𝑒_!"+ 𝛽_!𝐺𝑂𝑉𝑑_!" +

𝛽_!𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁_!"+ 𝛽_!"𝑂𝑃𝐸𝑁_!"+ 𝛽_!!𝑈𝑁𝐷𝐸𝑅_!"+ α_!+ ε_!" (𝟐) Furthermore, this thesis examines whether the augmented Solow model improves by including additional relevant variables.Regression 2 includes the same variables as regression 1, with an extension of the additional variables mentioned in chapter 2 of this research. 𝐺𝑂𝑉𝐸!" and

𝐺𝑂𝑉𝐷_!" are measures for government expenditure and government debt, respectively. 𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁_!" measures the GDP deflator, 𝑂𝑃𝐸𝑁_!" represents the openness to trade and 𝑈𝑁𝐷𝐸𝑅_!" determines the undervaluation of the exchange rate.

To perform a correct OLS regression, the regressions must meet certain assumptions (Stock & Watson, 2015, p. 588):

1. 𝐸 𝑢_! 𝑋_!) = 0,

2. 𝐸 𝑢_! 𝑌_!!!, 𝑋_!!! = 0, 3. 𝐶𝑜𝑟𝑟 𝑋_!, 𝑈_! = 0,

4. (𝑌_!, 𝑋_!!… . , 𝑋_!") have a stationary distribution, 5. There is no perfect multicollinearity,

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The assumptions of the model are tested in chapter 5.

3.1 Data

This section provides a detailed explanation of the relevant variables used in the two regressions. The data of this research is based on a balanced panel regression. Consequently, this paper does not take every country of the OECD into account. Appendix A of this research provides a list of all the 22 countries used in this paper. The (augmented) Solow growth model is a long-term growth model. That is why the timeframe of the empirical model of this research is from 1984 to 2014. In total, 30 years, which is enough for an analysis of long-term economic growth (Solow, 1956, p. 66).

The dependent variable is the first difference of GDP per capita, retrieved from the World Bank database1_{. The world GDP per capita comes from the World Bank database}2_{as well. The}

population growth is determined through the working-age population growth. This growth rate is not available. That is why I take the product of the working- age population percentage and population, and measure its growth. Both data sets are retrieved from the World Bank database3. The variables, δ and g, respectively called depreciation rate and technological change, are both a constant in the model. Together they are equal to 0.05. Human capital is determined by several factors. However, for the empirical model of this research, it is based on the gross enrollment ratio of secondary school (both sexes). This data is collected from the Unesco database4. The variables mentioned above are determined by the same approach as Mankiw, Romer & Weil (1992) do. One of the assumptions of the Solow growth model is that is based on a closed economy. In a closed economy are total investments equal to total savings (Westerhout, 2016). Therefore, the rate of savings devoted to capital can be measured by the gross capital formation as a percentage of GDP. Formerly known as the gross domestic investment rate. This data is retrieved from the World Bank database5_{. The GDP deflator is used as an indicator for inflation.}

The GDP deflator is computed as the ratio of GDP in current local currency to the GDP in constant local currency (World Bank, 2016). In addition to savings, this is collected from the

1_Source:_{http://data.worldbank.org/indicator/NY.GDP.PCAP.CD} 2_Source:_{http://data.worldbank.org/indicator/NY.GDP.PCAP.CD} 3_Source:_{http://data.worldbank.org/indicator/SP.POP.1564.TO.ZS}_&

http://data.worldbank.org/indicator/SP.POP.TOTL

4_Source:_{http://data.uis.unesco.org/Index.aspx?DataSetCode=EDULIT_DS} 5_Source:_{http://data.worldbank.org/indicator/NE.GDI.TOTL.ZS}

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World Bank database6_{as well. A better indicator of inflation is the consumer price index, since}

this is not available for every country and for every year, the GDP deflator is a good alternative. The inflation rate and the fraction of the savings rate that is devoted to capital are determined by the same approach as Barro & Sala-i-Martin (1992) do. For government expenditure, the general government final expenditure is used (Barro, 1989, pp. 15-16). This data comes from the World Bank database7. Government debt is determined by the total central government debt in

percentage of GDP (Chercherita-Westphal & Rother, 2012, pp. 1395-1396). This data is

provided by the IMF database8 and OECD database9. For some countries of this sample the IMF database misses a few years. Therefore, I get the undetermined years from the OECD database. The reason I am not using the whole timeframe just from the OECD database, is because the OECD stopped updating the data after 2010. The trade intensity, in other words, openness to trade, is measured as the ratio of export plus import to GDP (Yanikkaya, 2002, p. 67). The undervaluation of the exchange rate is measured through the real exchange rate minus the absolute purchasing power parity (Rodrik, 2008, p. 371). Both values are retrieved from the World Bank database10.

3.3 Panel regression

There are two types of data that can have a two-dimensional structure: pooled cross-sectional data and panel data. Both have a cross-cross-sectional dimension and a time-series dimension combined (Wooldrige, 2009, pp. 5-11). Panel data refers to observations for multiple entities, where each entity is observed in two or more periods. The main characteristic that distinguishes panel data from pooled cross-sectional data is that it observes data within cross sections of the same entities across a time period. While pooled cross-sectional data observe cross-sections, while every year is independently distributed. This means that for pooled cross-sectional data the coefficients of a pooled model can differ at each point in time (Bell & Jones, 2014, p. 135).

According to Wooldrige (2009) panel regressions have several advantages over pooled

6_Source:_{http://data.worldbank.org/indicator/NY.GDP.DEFL.KD.ZG} 7_Source:_{http://data.worldbank.org/indicator/NE.CON.GOVT.ZS}

8_Source:_{https://www.imf.org/external/pubs/ft/weo/2016/01/weodata/download.aspx} 9_Source:_{http://stats.oecd.org/Index.aspx?DataSetCode=GOV_DEBT}

10_Sources;_{http://data.worldbank.org/indicator/NE.IMP.GNFS.ZS}_&

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cross-sectional regressions. Panel data is useful since it can correct for unobserved time-invariant variables. Another advantage of panel data is that it allows us to study the importance of lagged variables. Lagged variables are variables with a time delay that are used to predict the current value of the dependent variable. It is important to include these sorts of variables because some variables only have an impact on the dependent variable after some time has passed. However, the presence of lagged variables comes with a problem, which is known as the Nickell bias. It biases the model since it creates a covariance between 𝑌_!,!!! and 𝜀_!" or 𝑌_!,!!! and 𝜀_!" (Hsiao, 2007, p. 11). The dash above the variable indicates as the average of a variable. Nevertheless, with a reasonable size T (30 years), there is no harm in estimating the regressors (Beck, Katz & Mignozetti, 2014, p. 278).

Because of the advantages of panel data over pooled cross-section data, this thesis makes use of a panel regression. Panel data can be analyzed with two regression models: a fixed effect model and random effect model.

Fixed effect model (FE)

𝑌

_!"

= 𝛽

_!

+ 𝛽

_!

𝑋

_!"

+ 𝛼

_!

+ 𝜀

_!"

𝑖 = 1, … … . , 𝑁; 𝑡 = 1, … … . , 𝑇

(12) A fixed effect regression is a conventional regression-based strategy to correct for an endogeneity bias (Hsiao, 2007, p. 4). Equation (12) contains a time-variant variable, 𝛽!𝑋!", and

time-invariant dummy, 𝛼_!. The time-invariant dummy represents the entity-specific variation that is constant across time. Compared to a pooled cross sectional model, the fixed effect model removes the time-invariant effects from the regression coefficients and puts this into a dummy variable, 𝛼_!. This dummy variable differs for every cross-section and is called the fixed effect (Bell & Jones, 2014, p. 138).There are different methods to measure the fixed effects, eventually the results of those methods are all the same. For this thesis the within fixed effect method is used. The within fixed effect method makes use of two equations. First, the results of equation (12) are calculated. After that, the average value of each variable, for each entity is subtracted from equation (12). Because of this the constant and time-invariant dummies cancel out.

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This research makes use of the characteristics of 22 different countries. Despite the fact that all those 22 countries are developed countries, some of those characteristics can differ across countries. For example, political systems or culture, which are relatively time invariant. By eliminating those fixed effects, an ordinary least square (OLS) method can be used.

Random effect model (RE)

𝑦

_!"

= 𝛽

_!

𝑥

_!"

+ 𝑎 + 𝜂

_!"

(12)

Where,

𝜂

_!"

= 𝛼

_!"

+ 𝜀

_!".

In contrast with the FE model, the RE model assumes that the time-invariant effects are random. Therefore, they are included in the error term (Greene, 2007, p. 183). In this case, the advantage of random effects is that the model does not cancel out the constant (Torres-Reyna, 2010). However, if the time-invariant dummies do correlate with the regressors, an FE model must be used. Otherwise, the coefficients of the regression will be biased.

In conclusion, reviewing the advantages of a panel model, I believe a panel regression with fixed effects or random effects is the best option to estimate the parameters of the empirical model of this research. The decision to choose for an FE model or RE model is discussed in chapter 4 of this research.

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Chapter 4: empirical results

GROWTH Regression 1 Regression 2 Independent variables Coef. (robust std. err.) t-value Coef. (robust std.err.) t-value CONSTANT .3488 (.1697) 2.06* (.1958) .0235 0.12 𝐥𝐧 (𝒍𝒂𝒈𝑮𝑫𝑷𝒑𝒄) -.1845 (.0282) -6.54* -.2358 (.0396) -5.95* 𝐥𝐧 (𝒘𝑮𝑫𝑷𝒑𝒄) -.1137 (.0132) 11.74* .1348 (.0109) 12.39* 𝐥𝐧 (𝒍𝒂𝒈𝒘𝑮𝑫𝑷𝒑𝒄) .1137 (0132) -8.59* -.1058 (.0135) -7.85* 𝐥𝐧 (𝑰𝑵𝑽𝑬𝑺𝑻) .2076 (.0497) 4.18* .1505 (.0457) 3.30* 𝐥𝐧 (∆𝑵𝑮𝑶) -.0324 (.0598) -0.54 -.1065 (.0506) -2.11* 𝐥𝐧 (𝑺𝑪𝑯𝑶𝑶𝑳) -.0026 (.0019) -1.36 -.0027 (.0027) -0.99 𝑮𝑶𝑽𝒆 -.0073 (.0034) -2.13* 𝑮𝑶𝑽𝒅 -.0076 (.0031) -2.49* 𝑰𝑵𝑭𝑳𝑨𝑻𝑰𝑶𝑵 -.0015 (.0003) -5.99* 𝑶𝑷𝑬𝑵 -.0018 (.0058) -1.86** 𝑼𝑵𝑫𝑬𝑹 -.0038 (.0006) -6.16* 𝐑𝟐_{− 𝐰𝐢𝐭𝐡𝐢𝐧} _0.5308 _𝐑𝟐_{− 𝐰𝐢𝐭𝐡𝐢𝐧} _0.5742 rho .6668 Rho .8209 F(6,21) 86.33* F(11,21) 75.55* MODEL FE MODEL FE Number of groups 22 Number of groups 22

Number of obs 660 Number of

obs 660 *Significant with a 5% critical value. **Significant with a 10% critical value.

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The table above illustrates the results of regression 1 and regression 2. Regression 1 shows the results of the augmented Solow growth regression. Regression 2 shows the results of the

extended augmented Solow growth regression. Both models are explained in chapter 3 of this paper.

According to the rho of regression 1, 86.33% of the variance is due to the differences across the panels. The 𝑅!_{-within is .5308.}_{This means that the independent variables of regression 1}

explain about 53.08% of the variation in the dependent variable. F(6,21) is equal to 86.33. This F-statistic shows that the hypothesis, whereby all the coefficients of the model are all equal to zero, can be rejected against a 5% significance level. It means that the all the variables combined are good at predicating the values of 𝐺𝑅𝑂𝑊𝑇𝐻_!"

However, when you take a closer look at each coefficient of regression 1, you can see that ln ∆𝑁𝐺𝑂 !" and ln 𝑆𝐶𝐻𝑂𝑂𝐿 !" do not have a significant impact, for a 5% or 10%

significance level. Therefore, it is not possible to make a good interpretation of the effect of those two variables on economic growth. The world GDP per capita and its lag are significant at 5% significance level. If the world GDP per capita goes up with 1%, economic growth goes down with -0.1137%. At the same time, when the first lag of world GDP per capita goes up with 1%, economic growth goes up with 0.1137%. It means that the short-term effect is negative. However, when time passes this effect turns into a positive effect. According to Solow (1956) there is a positive correlation between investment and economic growth. The empirical results in the table comply with this theory. Since a 1% increase in investments devoted to capital leads to a 0.2076% increase in economic growth.

To continue, the rho of regression 2 is equal to 82.09%. Speaking about the goodness-of-fit, the 𝑅!_{-within is equal to 0.5742. Both values are higher than the 𝑅}!_{-within and rho of}

regression 1. It means that the inclusion of the extra variables give the augmented Solow model a higher explanatory power. Furthermore, the F (11,21) is equal to 75.55, which proves that for a 5% significance level, the independent variables jointly affect the dependent variable.

However, according to the t-values, independently this is not the case for all the

variables. ln 𝑆𝐶𝐻𝑂𝑂𝐿 _!" cannot be rejected against a 5% or 10% significance level. Therefore, it is not possible to draw any conclusions about its effect on 𝐺𝑅𝑂𝑊𝑇𝐻!". Furthermore, 𝑂𝑃𝐸𝑁!" is

insignificant for a 5% significance level, yet significant for a 10% significance level.

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in chapter 2 of this research. Yannikaya (2002) shows that an increase in trade volume (𝑂𝑃𝐸𝑁!")

increases the GDP per capita, while the statistics of this research show the opposite. A possible explanation for this can be the trade barriers of a country. Import tariffs positively correlates with economic growth (Yannikaya, 2002, p. 78-79). From the 22 OECD countries of this sample are 12 countries member of the European Union. All those 12 countries are part of the single market. It means that in this single market there is a free movement of goods, services, capital and labor (Breuss, 2002, p. 254). Therefore, those 12 countries cannot impose import tariffs to its citizens, who want to buy products from other European Union countries. Possibly, this could lead to the negative coefficient of the variable 𝑂𝑃𝐸𝑁_!". ln 𝐼𝑁𝑉𝐸𝑆𝑇 _!" has, just as in regression 1 a positive relationship with economic growth. However, the coefficient does decrease in value. This happens, because ln 𝐼𝑁𝑉𝐸𝑆𝑇 _!" correlates with the extra variables, which are omitted in

regression 1. Omitting those extra variables leads to an overstated coefficient (Stock & Watson, 2015, p. 229). 𝐺𝑂𝑉𝑒_!" has a negative effect on 𝐺𝑅𝑂𝑊𝑇𝐻_!". A 1-unit increase in government expenditure decreases economic growth with 0.73%. This is in line with the theory of Barro (1991) and Ludvigson (1996), mentioned in chapter 2 of this paper. Consequently, it is not in agreement with Mankiw’s (2013) theory. The researcher shows that government expenditure has a positive effect on economic growth on the basis of the Keynesian cross model.𝐺𝑂𝑉𝑑_!" has a negative effect on growth. A 1-unit increase in government debt is associated with a decrease in economic growth of - 0.73%. There are 12 EU countries in this sample. According to the

Maastricht treaty, made in 1993, the EU members are allowed to have a gross government debt of only 60% (Pilbeam, 2013, pp. 425-427). Checherita-Westphal & Rother (2012) say that government debt only influences economic growth if it is at least 90% of its GDP ratio. After the financial crisis in 2008 many financial institutions came into a liquidity crisis. To help those institutions, many EU countries violated the Maastricht treaty in order to bail them out (Pilbeam, 2013, p. 437-442). Those bailouts increased the government debt to GDP ratio of those countries above 60%. Because of those bailouts, the government debt to GDP ratio of many EU countries increased to a percentage above the 60% rule. This can be one of the reasons why the coefficient of 𝐺𝑂𝑉𝑑_!" is negative. The variable 𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁_!" is significant for a significance level of 5%. For each additional unit of 𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁!" , 𝐺𝑅𝑂𝑊𝑇𝐻!" decreases with -0.15%. The sign is in

line with Fisher’s (1993) theory. Mentioned in chapter 2 of this research. An 1-unit increase in 𝑈𝑁𝐷𝐸𝑅_!", goes with a -0.38% decrease in 𝐺𝑅𝑂𝑊𝑇𝐻_!". This is not in agreement with Rodrik’s

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(2008) theory. He shows that the undervaluation of the exchange rate a positive effect has on economic growth. This paper does not make the distinction between a fixed exchange rate regime and a floating exchange rate regime, which can be a possible explanation for the variable’s negative coefficient. According to Levy-Yeyati and Sturzenegger (2003), after the Bretton Woods period, countries that had a flexible exchange rate regime had slower growth and greater output volatility. More importantly, from the 12 EU-members of this sample, 8 countries are member of the European Economic and Monetary Union. Those countries have the same currency, and thereforethe same undervaluation of the exchange rate. It creates little volatility in the regression. That is why it can give a distorted illustration of the actual relationship between the two variables.

Chapter 5: sensitivity analysis

To determine if the empirical model of this research follows the six OLS assumptions, given in subsection 3.2, a sensitivity analysis is performed.

Serial (auto) correlation exists if the error term is correlated across time. It makes the results less efficient and biases the standard errors. It is usually found in time series data. This does not necessarily mean that the error term is correlated across entities, only across time. A test for the detection of serial correlation is the Breusch-Godfrey test. However, it does not work on multiple panels (Wooldrige, 2009, p. 418). That is why it cannot be used in this research.

Wooldrige (2002) developed an alternative for this test, which is known as the Wooldrige test. If 𝜀_!" does not contain first order serial correlation, the 𝑐𝑜𝑟𝑟 ∆𝜀_!", ∆𝜀_!"!! = −5 (Drukker, 2003, pp. 168-169).

The p-value is 0.0000. Therefore, it can be rejected for a significance level of 5%. This means that the data deals with first-order autocorrelation.

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Another problem occurs if the error term is correlated across entities. If the observed data makes use of homoscedastic standard errors, while it actually has heteroscedastic standard errors, the t-values of the regression will be biased. It means that the t-statistics are no longer good for interpretation (Stock & Watson, 2015, p. 375). To test for heteroskedasticity, I use the Breusch-Pagan Lagrange multiplier test. It is designed to test for heteroscedasticity for linear panel regressions. The usual heteroskedastic-robust standard error or the homoscedastic-nonrobust standard errors for a cross-sectional linear regression are not valid for panel regressions (Greene, 2007, pp. 165-167).

With a chi-squared distribution and a significance level of 5%, the null hypothesis can be rejected. This means that the data of this research deals with heteroskedasticity.

To correct for heteroskedasticity and autocorrelation, the heteroskedasticity- and autocorrelation consistent (HAC) standard error should be used. It is a clustered standard error, which allows an arbitrary correlation within a cluster, but assumes zero correlation across clusters. This way, it can allow heteroskedasticity and autocorrelation, without producing biased t-values. The clustered standard error can be used for homoscedastic error terms as well.

However, the disadvantage of a clustered standard error is that it will be less efficient than the normal homoscedastic standard error for auto-correlated panel data. Nonetheless, in most empirical analyses homoscedasticity does not exist. (Stock & Watson, 2015, pp. 413-414).

Times series are stationary if its probability distribution does not change over time. It regresses to a set mean and set variance, without an alteration over time. When the data is non-stationary, the mean and the variance follow a stochastic trend. This “random walk”, leads to several problems. First, the least square assumptions for time series do not hold, which makes the autoregressive coefficients biased. Secondly, the data has no longer a normal distribution, even in big samples. In addition, it can lead to a spurious regression. This occurs when two time series appears to be related, while in reality they are not (Stock & Watson, 2015, pp 600- 602).

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The Im-Pesaran-Shin unit root test is designed to examine whether the data contains a unit-root or not.

The test is tailored for heterogeneous multiple panel data and is based on the mean of the Dickey-Fuller unit root test. If the null hypothesis can be rejected the data does not contains a unit-root. If it cannot be rejected the data does contain a unit-root (Im, Persan & Shin, 2003, pp. 53-55).

the data above shows a statistic of -14.7272. Therefore, with a significance level of 5%, the null hypothesis can be rejected. Therefore, the dependent variable does not contain a unit-root.

To know whether the independent variables of the empirical model of this research contain a unit-root or not, I carry out the same test on each independent variable as well. You can find an overview of those test statistics in Appendix B of this research.

According to this overview, ln (𝑁𝐺𝑂)_!" contains a unit- root. This non-stationary problem can be resolved by replacing ln (𝑁𝐺𝑂)!"with its first difference.

After the Im-Pesaran-Shin unit root test, it is important to know which model is valid to perform the regression, the fixed-effect model or the random-effect model. Assuming that the time-invariant dummies are correlated with the independent variables, FE would be the correct option. If they are uncorrelated, RE should be used. For practicalities, the fixed effects approach is costly in degrees of freedom. However, most of the time, there is little justification that the dummies are uncorrelated with the independent variables. In order to know which model

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estimates the parameters of the empirical model the best, I make use the Hausman specification test.If the chi-squared test statistic can be rejected, the fixed effect model should be used. If the null hypothesis cannot be rejected, the random effect model should be used (Greene, 2007, pp. 208-210).

The test has a chi-square statistic of 334.45. Therefore, with a 5% significance level, the null hypothesis can be rejected. Accordingly, the fixed effect model should be used for this research

In conclusion, after performing the Wooldridge test, Breush-Pagan test,

Im-Pesaran-Shim test and the Hausman specification test, the conclusion is that the variables are estimated with a fixed effect model. Secondly, a clustered standard error is used, to correct for

autocorrelation and heteroskedasticity. Furthermore, ln (𝑁𝐺𝑂)_!" is replaced by the variable ln (∆𝑁𝐺𝑂)_!", which is the first derivative of ln (𝑁𝐺𝑂)_!".

Chapter 6: conclusion

This thesis examines whether the augmented Solow growth model still holds in the period 1984-2014 for 22 OECD countries. Furthermore, it examines whether the model’s

explanatory power improves by adding additional relevant variables. The additional variables are government expenditure, inflation, government debt, openness to trade and the undervaluation of the exchange rate.

The augmented Solow growth regression (regression 1) does not show clear evidence that the model still holds. The population growth rate and human capital are insignificant. Therefore, it is not possible to draw any conclusions about their effects on economic growth. The extended augmented Solow growth regression (regression 2) has a higher explanatory power than the augmented Solow growth regression. This means that the additional variables mentioned above

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jointly improve the performance of the augmented Solow growth model. The 𝑅!_{-within goes up}

from 0.5308 for the augmented Solow growth model to 0.5742 for the extended augmented Solow growth model. Furthermore, it can be concluded that the fraction of savings devoted to capital has a positive effect on economic growth. Both for the augmented Solow growth regression and the extended augmented Solow growth regression it is significant positively correlated with economic growth. Inflation, government expenditure and government debt have also a significant effect on economic growth. In contrast to the augmented Solow growth regression has the population growth rate a significant negatively effect on economic growth in the extended augmented Solow growth regression. The undervaluation of the exchange rate and the openness to trade show different results than existing literature predicts. Both for the

augmented Solow growth regression and the extended augmented Solow growth regression is human capital insignificant. So a good interpretation of this variable cannot be made.

This paper gives insight on the statistics of 22 countries. All those countries are

developed countries. Herewith, it cannot say something about the external validity of the results. It cannot be implied that those results are applicable to developing countries as well. Next, although I add five extra variables to the standard augmented Solow growth model that does not mean that other unexplained factors do no contribute to economic growth. It is possible that the empirical model of this research has an omitted variable bias. Further research should be done on which variables to include in a typical growth regression. Finally, one should increase the sample size and number of included countries in future research.

Bibliography

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Barro, R.J (1991). Economic growth in a cross section of Countries. The quartily journal

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Barro, R. J., & Sali-i-Martin, X. (1992). Convergence. Journal of Political Economy, 100(1), pp. 223-251.

Barro, R.J. (1995). Inflation and economic growth. (NBER Working Paper No. 5326). Cambridge, MA: National Bureau of Economic Research

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Checherita-Westphal, C., & Rother, P. (2012). The impact of high government debt on economic growth and its channels: An empirical investigation for the euro area. Euorpean

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Drukker, D. M. (2003). Testing for serial correlation in linear panel-data. The Stata Journal, 3(1), pp. 168-177.

Esarey, J., & Menger, A. (2016). Practical and Effective Approaches to Dealing with Clustered Data. Department of Political Science, Rice University, Unpublished Manuscript.

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Economics, 32(1993), pp. 485-512.

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Feder, G. (1982). On exports and economic growth. Journal of Development Economics

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Im. K. S., Pesaran, M. H., & Shin, Y. (2003). Testing for unit roots in heterogeneous panels.

Journal of Econometrics 115(2003) pp. 53-7.

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Rate Regimes on Growth

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2(1971), pp. 485-498.

Rodrik, D. (2008). The Real Exchange Rate and Economic Growth. Brookings Papers on

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Van Ophem, H. (2016). Lecture 4: Functional Form and Validity. Retrieved from:

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Appendix A

Appendix A gives an overview of all the 22 countries that participates in this research. Each country of the list is a member of the OECD since 1960.

List OECD countries

Austria France The Netherlands The United Kingdom Mexico Turkey

Belgium Greece Portugal Canada New Zealand Iceland

Denmark Ireland Spain Japan Norway

Finland Italy Sweden The Republic of Korea Switzerland

Appendix B

Appendix B gives an overview of the Im-Pesaran-Shin unit root test on the independent variables of this research

H0: All panels contains unitroots Number of panels:

22

H1: Some panels are stationary Number of periods:

31

Panel means: Included Time trend: Included

Variable

ln 𝑤𝐺𝐷𝑃𝑝𝑐 !" -4.4221*

ln (𝐼𝑁𝑉𝐸𝑆𝑇)_!" -2.1316*

ln (𝑁𝐺𝑂)_!" -1.5549

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28 𝐺𝑂𝑉𝑒!" -18.2676* 𝐺𝑂𝑉𝑑!" -4.8330* 𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁!" -4.5277* 𝑂𝑃𝐸𝑁!" -10.8770* 𝑈𝑁𝐷𝐸𝑅!" Not available

*Significant at 5% critical value

Economic growth: an extension of the augmented Solow growth model : empirical analysis of 22 OECD countries