Government Size and Intersectoral Income Fluctuation: An International Panel Analysis

Daehaeng Kim; Chul-In Lee

doi:10.5089/9781451866575.001.A001

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Government Size and Intersectoral Income Fluctuation: An International Panel Analysis

Author: Mr. Daehaeng Kim and Chul-In Lee¹

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Author’s E-Mail Address: DKIM2@IMF.ORG

Publication Date:: 01 Apr 2007

eISBN:: 9781451866575

Language:: English

Keywords:: WP; government spending; open economy

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Using the between-sector variation in income as a new measure of economic uncertainty, this paper proposes simple models and supportive empirical evidence for the causal relations between economic uncertainty and government size in the open economy setting. Key empirical findings include: (1) a larger government reduces economic uncertainty, and, at the same time, (2) an economy facing higher uncertainty has a larger government. However, (3) the government tends to resort to redistributive policies to reduce the uncertainty, while (4) government direct spending is also an effective option for the purpose. The study also finds that (5) cross-sectional measure of economic uncertainty tends to rise when a country becomes more open to international trade.

Abstract

I. Introduction

Economic stabilization has been a major topic in macroeconomics and public economics, because of its implications for economic growth and welfare.² In principle, individuals can overcome the negative impact of economic fluctuations through portfolio diversification in capital markets or through transactions in credit markets. However, empirical research finds that market mechanisms do not provide perfect protection for individuals against economic uncertainty. The finding of imperfect risk sharing through private markets is in general attributed to the fact that contracts for managing individual economic uncertainty are often subject to asymmetric information problems such as moral hazard or adverse selection.³ This ‘market failure’ argument suggests that there exists scope for further income smoothing by government intervention.

The traditional view on the stabilization role of government has focused on the ability of the tax and transfer system to stabilize disposable income (Sachs and Sala-i-Martin, 1992; von Hagen, 1992; Bayoumi and Masson, 1995). According to simple Keynesian models, fluctuations in gross income can be partially smoothed by cyclical changes in taxes and transfers over business cycles so that disposable income is less volatile than gross income. However, recent empirical studies by Gali (1994) and Fatas and Mihov (2001) show that increasing the size of government reduces the volatility of gross income as well as disposable income.⁴

Against this backdrop, some economists recognize a possible reverse causality between economic uncertainty and the shares of various government operations in GDP. In his influential study addressing why more open economies have larger governments, Rodrik (1998) proposes the following two hypotheses: (i) greater exposure to external risk increases the total risk to which residents of an economy are exposed; and (ii) societies that face more economic uncertainty demand a larger size of government as social insurance. While Rodrik’s hypotheses call for the need to control endogeneity of government size—otherwise, the estimated impact of government size on economic uncertainty is subject to a simultaneous equation bias—no empirical studies explicitly explore the causal effects of economic uncertainty on various measures of government size.

Our study advances the existing literature in two aspects. First, it proposes a new measure of economic uncertainty. In this study, income risk for workers in particular sectors is measured by intersectoral income fluctuation, which is defined as the second moment of the cross-sectional distribution of sectoral labor income growth rates. Intersectoral income fluctuation has two advantages over the variance of GDP growth rates measure that has been used in previous studies: (1) it captures a comparable but different aspect of economic uncertainty—the sector-specific microeconomic risks, which may be a more important concern for individuals in the context of private or social insurance; and (2) it facilitates using panel estimation techniques that can separate the true effect from region-specific fixed effects and year-specific effects.⁵

The second contribution of this paper is that it proposes a unified empirical framework to explore the interactions between government size, economic uncertainty and openness to trade. Specifically, our model specification allows us to answer several key questions on the stabilization role of government, including (1) whether government size can affect the economic uncertainty to which individuals in an economy are exposed; (2) if so, which type of government expenditure is more effective in reducing economic uncertainty; (3) conversely, whether the economy facing higher economic uncertainty has a larger size of government; (4) in that case, which type of government expenditure is more responsive to the stabilization purpose; and (5) how openness to trade affects economic uncertainty and the transformation of external shocks to intersectoral income fluctuation.

Our empirical results lead us to the following conclusions. First, the size of government reduces intersectoral income volatility, and, at the same time, an economy facing higher intersectoral income fluctuation has a larger government. Second, the government tends to resort to redistributive policies rather than expenditure less subsidies and transfers to reduce economic uncertainty, while the latter is almost as effective as government subsidies and transfers in reducing intersectoral income fluctuation. Third, intersectoral income fluctuation increases when a country becomes more open to international trade, and increases further as an economy is exposed to more intense external shocks. Finally, the effect of external shocks on intersectoral income fluctuation depends on an economy’s openness to trade with external shocks increasing intersectoral income fluctuation in economies where the trade share in GDP is larger than about 50 percent and decreasing it in less open economies.

The rest of the paper proceeds as follows. Section II provides the analytical framework for the empirical analysis. Based on the framework, we discuss the theoretical relationship between government size, sector-specific income risks, and openness to trade. The specification and identification of empirical models are also discussed in this section. Section III describes the data that econometric analysis uses, and then presents estimation results. Conclusions are given in Section IV.

II. Theoretical Framework

A. Measurement of Economic Uncertainty

In macroeconomic cross-country studies the extent of economic uncertainty faced by economic agents is commonly measured by the variance of GDP growth rates. However, a crucial problem of this measure is that it provides information on ‘macroeconomic’ stability only. Since a substantial portion of sector-specific income shocks can be offset in the process of aggregation, the variance of aggregate income can be small even when sector-specific income risk is high. This tendency would be more prominent when asymmetric sector-specific shocks are a dominant source of economic uncertainty.⁶ In this respect, intersectoral income fluctuation (IIF) can show a different aspect of economic uncertainty by capturing the intensity of sector-specific income risks. In fact the data used in our empirical analysis indicate that there is a positive, but statistically insignificant, correlation between IIF and the variance of GDP growth rates (Figure 1). However, the positive correlation is mostly driven by a couple of observations (South Korea and Finland); and without this observation, we would not see a clear relationship between macro and microeconomic measures of economic uncertainty.

Another advantage of our new measure is that it can show a clear link between government size, economic uncertainty and openness to trade. Since external shocks in an open economy are likely to be sector-specific, sector-specific income risks would be more intense when an economy is more integrated into international markets. However, these hypotheses in the open economy context cannot be properly tested without relying on a cross-sectoral measure of economic uncertainty like IIF. Against this background, we present two models in this section, which set guidelines for a unified empirical framework by delineating the interactions between government size, economic uncertainty and openness to trade.

B. Simple Keynesian Model

There have been a few attempts to conduct a theoretical analysis on the stabilization role of government size. One of the theoretical papers is Gali (1994), which considers the effects of steady-state government spending on GDP volatility. In his stochastic dynamic general equilibrium model, Gali (1994) identifies various effects of government size. Since his analysis is based on a real business cycle model with flexible prices and market clearing, the only way that ‘acyclical’ government spending can stabilize income is through affecting the optimal behavior of individuals. However, the theoretical relationship proposed by his model is ambiguous, since results are sensitive to parameter values. Moreover, the quantitative importance of government spending would be very small compared to empirical findings, even with the most favorable configuration of parameter values.

To derive simple but clear implications, we adopt a Keynesian approach where the demand side of an economy determines the equilibrium level of income.⁷ In the model, income per capita of sector i (y_it) is assumed to consist of incomes from the private sector demand and government spending. On average, the private-sector incomes grow at the rate of θ, and the shocks to the private-sector income growth rate of sector i (ε_it) have the following properties: $E (ε_{it} | t) = μ_{t}, var (ε_{it} | t) = σ_{ε}^{2}, and cov (ε_{it}, ε_{jt} | t) = 0$ for all i and j.⁸ These assumptions describe the statistical properties of the cross-sectional distribution of private-sector income growth rates. On average, each sector is exposed to a common income shock – the mean of the cross-sectional distribution (μ_t). The intensity of sector-specific income shock is measured by the variance of the sectoral growth rate distribution $(σ_{ε}^{2})$ , which indicates how shocks to sectoral income growth rate spread around the common shock. Furthermore, we assume the unconditional properties are such that E(ε_it)=E(μ_t)=0, var(ε_it)=σ², and cov(ε_it, ε_jt)=0 for all i and j.

The next set of assumptions is on government spending. The government sets the growth rate of its spending equal to the steady state growth rate, θ Δ ln G_t = θ for all t, where G is the total government spending. This implies that government spending is “acyclical.” We also assume that the government sets the proportion of its spending allocated to sector i (α_i) equal to the proportion of sectoral income to aggregate income (γ_i): $α_{i} \equiv \frac{G_{i}}{G} = \frac{y_{i}}{y} \cdot n_{i} \equiv γ_{i},$ ⁹ where G_i is the government spending allocated to sector i, n_i is the share of sector i workers in total workers $(n_{i} \equiv \frac{N_{i}}{\sum_{j = 1}^{M} N_{j}}), N_{i}$ is the number of workers in sector i, M is the number of sectors in this economy, and $y \equiv \sum_{j = 1}^{M} n_{j} \cdot y_{j}$ is income per capita of this economy.¹⁰ Then, the growth rate of income per capita of sector i (Δ ln y_it) can be expressed as the weighted average of incomes that are earned from the private sector and generated from government spending.

\begin{matrix} Δ \ln y_{it} = (1 - λ_{i}) \cdot (θ + ε_{it}) + λ_{i} \cdot θ, & (1) \end{matrix}

where λ_i is the government share in sector i’s income, defined as ${\frac{G_{i}}{N_{i} \cdot y}}_{i}$ . These assumptions lead to the following results.¹¹

Result 1:

The sectoral government share (λ_i) is equal to the aggregate government share (λ) defined as the aggregate government spending over GDP. In our notation, this result can be written as $λ_{i} = λ \equiv \frac{G}{\sum_{j = 1}^{M} N_{j} \cdot y_{j}} .$

Result 2:

The growth rate of sector i’s income is Δ ln y_it = θ + (1–λ)·ε_it The conditional expectation and variance of sector i’s income growth are E(Δ ln y_it | t)= θ + (1–λ). μ_t and $var (Δ \ln y_{it} | t) = {(1 - λ)}^{2} \cdot σ_{ε}^{2},$ respectively.

Next, we define two sample means $({\bar{y}}^{n} and {\bar{y}}^{γ})$ and two sample variances $(s_{n}^{2} and s_{γ}^{2})$ of income growth rates as follows:

\begin{matrix} {\bar{y}}_{t}^{n} \equiv \sum_{j = 1}^{M} n_{j} \cdot Δ \ln y_{jt}, & {\bar{y}}_{t}^{γ} \equiv \sum_{j = 1}^{M} γ_{j} \cdot Δ \ln y_{jt}, \\ s_{n, t}^{2} \equiv \frac{\sum_{j = 1}^{M} n_{j} \cdot {(Δ \ln y_{jt} - {\bar{y}}_{t}^{n})}^{2}}{1 - \sum_{j = 1}^{M} n_{j}^{2}}, & s_{γ, t}^{2} \equiv \frac{\sum_{j = 1}^{M} γ_{j} \cdot (Δ \ln y_{jt} - {\bar{y}}_{t}^{γ})^{2}}{1 - \sum_{j = 1}^{M} γ_{j}^{2}} \\ . \end{matrix}

It should be noted that the employment shares of each sector (n_i) are used as weights in the computation of ${\bar{y}}^{n}$ and $s_{n}^{2}$ , while the income shares of each sector (γ_i) are used in the computation of ${\bar{y}}^{γ}$ and $s_{γ}^{2}$ .

Result 3:

The weighted averages of sectoral income growth rates, ${\bar{y}}_{t}^{n}$ and ${\bar{y}}_{t}^{γ}$ , are unbiased estimators of the population income growth rate conditional on time t, E(Δ ln y_it | t); $s_{n, t}^{2}$ and $s_{γ, t}^{2}$ are unbiased estimators of population variance of income growth rate, var(Δ ln y_it | t).

In our notation, $E ({\bar{y}}_{t}^{n} | t) = E ({\bar{y}}_{t}^{γ} | t) = E (Δ \ln y_{it} | t) = θ + (1 - λ) \cdot μ_{t}$ and $E (s_{n, t}^{2} | t) = E (s_{γ, t}^{2} | t) = var (Δ \ln y_{i t} | t) = {(1 - λ)}^{2} \cdot σ_{ε}^{2} .$

Result 4:

The unconditional expectation and variance of Δ ln y_it are E(Δ ln y_it) = θ and var (Δ ln y_it)=(1-λ)²·σ², respectively.

Two statistics defined as ${\hat{σ}}_{n}^{2} = \frac{1}{T} \cdot \sum_{t = 1}^{T} s_{n, t}^{2}$ and ${\hat{σ}}_{γ}^{2} = \frac{1}{T} \cdot \sum_{t = 1}^{T} s_{γ, t}^{2}$ are unbiased estimators of $var (Δ \ln y_{it}) : E ({\hat{σ}}_{n}^{2}) = {(1 = λ)}^{2} \cdot σ^{2} .$

In this model, the exact definition of intersectoral fluctuation is the conditional variance of sectoral income growth rate, var(Δ ln y_it |t). Using Result 2, we can derive the stabilization effect of government size. By differentiating var(Δ ln y_it |t) with respect to λ, we obtain:

\begin{matrix} \frac{\partial var (Δ \ln y_{it} | t)}{\partial λ} = - 2 \cdot (1 - λ) . σ_{ε}^{2} < 0 . & (2) \end{matrix}

This implies that an economy with a larger government has smaller sectoral income volatility. When the government share in sectoral income is constant, it serves as a symmetric part of sectoral income. For this reason, as government size becomes larger, the symmetric component of sectoral income increases, and thus sectoral income volatility becomes smaller.

On the other hand, the reverse causality can be also discussed using this relationship, while it is not explicitly considered in the previous model. From Result 2, we see that an economy achieves the minimum level of intersectoral fluctuation when the government sets its share equal to 1 (λ = 1). However, the government will not push the income-risks-minimizing motive to its limit since increasing government size is likely to impose some real costs.¹² Suppose, for example, government’s optimization problem can be expressed as maximizing the value of a linear combination of real activity of the economy, Γ(λ), and the conditional variance of sectoral income growth rates:

$V (λ; σ_{ε}^{2}) = A ּ Γ (λ) - B ּ {(1 - λ)}^{2} ּ σ_{ε}^{2}$ , where A and B are positive and, Γ’(·)<0. When government maximizes its objective function $V (λ; σ_{ε}^{2})$ given the underlying asymmetric income shock $σ_{ε}^{2}$ , the optimal size of government (λ^*) satisfies $A \cdot Γ ´ (λ^{*}) + 2 B ּ (1 - λ^{*}) ּ σ_{ε}^{2} = 0$ and λ^*∈ (0,1). Differentiating this optimality condition, we can draw an implication on how the government responds to an increase in the underlying sector-specific income risks $σ_{ε}^{2} :$ ¹³

\begin{matrix} \frac{d λ^{*}}{d σ_{ε}^{2}} = \frac{- 2 \cdot B \cdot (1 - λ^{*})}{A \cdot Γ ″ (λ^{*}) - 2 \cdot B \cdot σ_{ε}^{2}} > 0 . & (3) \end{matrix}

This equation shows that the government facing greater sector-specific income risks tends to spend more in equilibrium. In a later section, we will test the implications derived by equations (2) and (3).

While our simple model can deal with the interactions between government size and intersectoral fluctuation well, it does not provide much insight to the case of the open economy due to its simplicity. Perhaps, the underlying relationship between uncertainty and government size would not change, but the extent to which a shock affects sectoral variation in income may intensify in a more open economy. The following subsection offers a simple open economy model, and highlights the importance of openness.

C. Openness to Trade and Intersectoral Fluctuation

To examine how openness to trade affects intersectoral fluctuation of labor income growth rates, we compare two economies that are identical except their trade policies. Those economies have two final goods (X₁ and X₂) and one intermediate good (Z). Final goods are domestically produced and consumed while intermediate good cannot be domestically produced.

These economies have two types of workers, and their skills are sector-specific and country-specific. For this reason, labor is immobile across sectors and countries.¹⁴ The number of type 1 workers is N₁, and that of type 2 workers is N₂. In addition, each worker is assumed to live only one period, providing one unit of labor inelastically. The Cobb-Douglas utility function represents the preferences of consumers. The consumer optimization problem is set up as follows.

\begin{matrix} \begin{array}{l} \max_{{x_{1 i}, x_{2 i}}} x_{1 i}^{α} ּ x_{2 i}^{1 - α} \\ s . t . w_{i} = x_{1 i} + p ּ x_{2 i} for i = 1 and 2 \end{array} & (4) \end{matrix}

The subscript i indicates the type of workers. w is the labor income, and p is the price of the second final good (X₂). We set the price of the first final good (X₁) equal to unity.

Each final good is produced with a constant return to scale (CRS) technology. Inputs are intermediate good and labor. The specific production functions are as follows.

\begin{matrix} x_{1} = A_{1} ּ Z_{1}^{γ} ּ L_{1}^{1 - γ} and x_{2} = A_{2} ּ Z_{2}^{β} ּ L_{2}^{1 - β} & (5) \end{matrix}

As represent the technology level of each sector, and we assume that A₁ < A₂without loss of generality. L is labor, and Z is an intermediate good. γ and β are the intermediate good shares in the production of X₁ and X_2, respectively. In the next step, we assume that one country (economy R) prohibits the international trade of the final good X₁ while there is no restriction to the trade of X₂. The other country (economy F) is assumed to have no trade restriction.¹⁵

Closing this model, we assume that these economies have two sources of economic shocks. The first is the technology shocks to A₁ and A₂, and the second is the external shocks to $p_{1}^{W}, p_{2}^{W}, and p_{z}$ . For simplicity, we assume that the productivity levels are stationary, all the random variables follow lognormal distribution, and they are not correlated with each other.

\ln A_{i} \sim N (μ_{A_{i}}, σ_{A_{i}}^{2}) and \ln p_{i}^{w} \sim N (μ_{P_{i}^{w}}, σ_{P_{i}^{W}}^{2}) for i = 1 and 2, and \ln p_{z} \sim N (μ_{P_{Z}}, σ_{P_{Z}}^{2}),

where μ_Y and $σ_{Y}^{2}$ are mean and variance of the random variable Y. Since we assume that all the exogenous variables are stationary, the percentage deviation of a variable Y from its steady state is defined as Ỹ ≡ ln Y −E ln Y. Following this notion, we can derive the covariance of labor income fluctuations in economy R and economy F.

\begin{array}{l} cov ({\tilde{w}}_{1}^{R}, {\tilde{w}}_{2}^{R}) = \frac{1 - 2 ּ γ}{{(1 - γ)}^{3}} ּ σ_{A_{1}}^{2} + {(\frac{γ}{1 - γ})}^{2} ּ (1 - δ) ּ σ_{p_{2}^{W}}^{2} + (\frac{γ}{1 - γ}) ּ (1 - δ) ּ σ_{pz}^{2} \\ cov ({\tilde{w}}_{1}^{F}, {\tilde{w}}_{2}^{F}) = \frac{- γ}{1 - γ} ּ σ_{p_{1}^{W}}^{2} + \frac{γ ּ β}{(1 - γ) ּ (1 - β)} ּ σ_{pz}^{2}, where δ \equiv \frac{γ}{1 - γ} - \frac{β}{1 - β} & (6) \end{array}

Result 5:

When the shares of imported factor are similar across sectors (γ ≈ β), and they are not greater than 50 percent, economy R’s covariance of labor income fluctuations between sectors is larger than that of economy F. At the same time, openness to trade will be higher in economy F.

Result 5 indicates that under certain conditions, the economy with trade restriction has stronger co-movement of labor income growth rates and less openness to trade. This implies that less open economy has smaller sectoral labor income volatility.¹⁶ The effect of openness to trade on intersectoral fluctuation primarily results from the differences in price flexibility. As mentioned above, labor is immobile, and therefore wage equalization does not hold in these economies. In this case, another channel through which sector-specific shocks diffuse into the whole economy is the adjustment of final goods prices. In the open economy, the domestic relative price of final goods is fixed at the international relative price. For this reason, sector-specific shocks do not proportionally affect labor incomes, and thus they eventually lead to asymmetric income fluctuations. On the other hand, the economy with trade restriction has more correlated labor income fluctuations between sectors since sector-specific shocks can affect labor income of the other sector through relative (domestic) price adjustment.

Equation (6) also provides some intuitions on how different the effects of external shocks can be in these two economies. In the model, we have three kinds of external shock: shocks to each of two final goods and a shock to the intermediate good. Suppose that the shares of imported factor are similar in two sectors, and they are smaller than 50 percent in both sectors (γ ≈ β < 0.5). In this case, we can see that an increase in the shock to the intermediate good price $(σ_{pz}^{2})$ has a positive effect on the covariance of intersectoral income volatility in both economies. Since the intermediate good is used in both sectors, the external shock to the intermediate good price works as a symmetric shock in these economies.¹⁷

However, the external shocks to final good prices have different effect on intersectoral fluctuation in these economies. As we can see from equation (6), the external shocks to final good prices work as a common shock in economy R, while they work as a sector-specific shock in economy F. Since domestic price adjustment mechanism works in the economy with trade restriction, favorable (unfavorable) external shocks to X₂ increase (decrease) labor incomes not only in sector 2 but also in sector 1. On the other hand, the external shocks to the price of X₁ boost intersectoral fluctuation in the open economy since they hardly affect the labor income of sector 2.

Result 6:

In economy F, the import of X₁ increases as sectoral difference in the productivity levels rises.

Another important result of this model is that as sectoral productivity difference increases, production of the final good with lower productivity is more likely to fall short of domestic demand for the good. This finding is analogous to conventional trade theories: economies specialize themselves to the industry where they have comparative advantage. Therefore, the modeled economy imports X₁ due to low productivity in the domestic production. The trade barrier assumed in the model can be rationalized in this situation because many governments regulate international trade in order to protect low-productivity (often called ‘infant’) industries.¹⁸

In sum, the model shows that under reasonable conditions: (i) the more open an economy is, the larger intersectoral fluctuation; (ii) external shocks are likely to decrease intersectoral fluctuation in less open economies while they can increase intersectoral fluctuation in more open economies; (iii) the trade pattern and policy of an economy can be affected by sectoral difference in the productivity levels; and (iv) these tendencies become more prominent as the intermediate good shares, γ and β, get close to zero.

III. Empirical Models and Data

A. Specification and Identification of Empirical Models

The baseline equations for intersectoral fluctuation and government expenditure, respectively, are as follows:

\begin{matrix} {ASY}_{jt} = c_{j} + y_{t} + α_{1} {GOV}_{jt} + α_{2} {OPN}_{jt} + α_{3} {OPN}_{jt} ּ {TOT}_{jt} + α_{4} {TOT}_{jt} + v_{jt} & (7) \end{matrix}

\begin{matrix} {GOV}_{jt} = c_{j}^{'} + y_{t}^{'} + β_{1} {ASY}_{j t} + β_{2} {DEP}_{jt} + β_{3} {INC}_{jt} + β_{4} {POP}_{jt} + β_{5} {LND}_{jt} + u_{jt} & (8) \end{matrix}

where subscripts j and t stand for country and year, respectively; v and u are the error terms of the system of equations; ASY = intersectoral income fluctuation; GOV = government size; y_t= year t specific intercept; c_j= region j specific intercept; OPN = openness to trade; TOT = terms of trade shock; DEP = dependency ratio; INC = log of real GDP per capita; POP = log of population; and LND = log of land area in square kilometer.

Equation (7) shows the sources of intersectoral income fluctuation, ASY, which we measure as the sample standard deviation of sectoral income growth rates (see below). As shown in equation (2), the size of government reduces intersectoral fluctuation, and thus we expect the coefficient α₁ <0. Equation (7) also regards openness to trade, external shocks and their interaction as important determinants of intersectoral fluctuations. As discussed in Section II.C, more open economies have larger intersectoral fluctuations. Moreover, the effect of external shocks on intersectoral fluctuation depends on the openness to trade: external shocks are likely to decrease sector-specific income risks in less open economies while they can increase the risks in more open economies. For this reason, openness to trade, terms of trade shocks, and their interaction are included in the equation. Based on the argument in Section II.C, we expect α₂ > 0, α₃ > 0 and α₄ <0. The economic interpretation of these coefficients will be further discussed in the next section.

The second equation of our system, equation (8), is an extension to the usual model of the determinants of government size. The main difference is the addition of intersectoral income fluctuations due to the theoretical result from equation (3) that governments facing larger intersectoral fluctuation tend to spend more. We thus expect β₁ > 0. Other variables are those typically considered in the literature. The log of real GDP per capita is included to examine Wagner’s law that the demand for government services is income elastic, so that the share of government expenditure is expected to rise with income. There is also a vast political economy literature that studies the determinants of government size. Alesina and Spolaore (1997) suggest that smaller countries will have a larger government as a percentage of GDP because of fixed costs in setting up a government. We measure this using log of population and log of land area in square kilometer. Another explanatory variable is the dependency ratio, defined as the share of non-working population in total population.

In addition to these explanatory variables, dummy variables are added to both equations (7) and (8) to capture region-specific fixed effects and year-specific effects. These effects are likely to be correlated with the key variables of interest, government size and uncertainty of an economy, making statistical inference on the relationship between government size and uncertainty difficult in the previous cross-sectional studies that use the variance of GDP growth rates. Using the intersectoral income fluctuation thereby allows a panel study that can separate the true effect from region-specific fixed effects and year-specific effects.

Endogeneity of openness to trade

As discussed in Sections II.B and presented in equations (7) and (8), the system of regression equations allows for endogenous relations between government size and intersectoral income volatility. Furthermore, our discussion in Section II.C reveals that openness to trade in the system is also likely to be endogenously determined: given that openness to trade is a determinant of intersectoral income volatility, a government may want to implement restrictive trade policies as well as spend more when it intends to reduce economic uncertainty. As a result, not only the size of government but also the extent to which an economy is integrated with the rest of the world is likely to interact with the sector-specific income risks facing the economy.

The most approach to handling the endogeneity problem of trade openness is that of Frankel and Romer (1999) who construct an instrument for international trade/GDP ratios by projecting bilateral trade flows on geographical characteristics that are “as exogenous a determinant as an economist can ever hope to get.” However, this approach fails to capture time series variations of openness to trade.¹⁹ Accordingly, we use sectoral productivity differences as an instrument variable (IV) to handle the possible endogeneity of openness to trade. This follows from our earlier Result 6 that international trade policy may be affected by sectoral productivity differences. According to conventional trade theories, an economy with higher sectoral productivity difference is better off with more involvement in international trade. Through international trade, the economy specializes in more productive sectors, and as a result, the overall welfare of the economy can be improved. However, trade liberalization does not necessarily lead to welfare improvement if labor mobility of an economy is limited. In such cases, the government may want to protect low-productivity industries by implementing restrictive trade policies. In the presence of opposing impacts on welfare, the actual effect of sectoral productivity difference on the openness to trade should be answered by empirical analysis.²⁰

Estimation strategy

The identification strategy for estimating equations (7) and (8) is that we first attempt to estimate each equation using possible IVs. If test statistics combined with theory lend support to identification of each of the equations, we then conduct joint 3SLS estimation. As suggested in Sections II.B and II.C, intersectoral income fluctuations, government size, and openness to trade are endogenous variables in the system of equations. These endogenous variables are affected by exogenous variables in direct and indirect ways. For many variables, their exogeneity is unambiguous. For example, reverse feedbacks toward dependency ratio, population, land area, and terms of trade shocks are not likely. However, we need more rigorous justification for some other variables such as income level and sectoral productivity difference. We thus do not rely on a particular set of identifying assumptions; rather we begin with an erroneous specification (e.g., OLS), and then examine how corrections using IVs improve the results, followed by the discussion on the validity of identifying assumptions.

Discussion on identifying assumptions: the preferred specification

Many economists have emphasized the role of international trade as a driver of productivity change.²¹ According to this view, openness to trade has a positive effect on productivity and income, which implies that we cannot easily rule out the causality running from international trade to income and sectoral productivity difference. On the other hand, Rodrik, Subramanian, and Trebbi (2004) shows that openness to trade is almost always insignificant and often enters the income equation with the “wrong” (i.e., negative) sign, suggesting that the positive effect of trade reported in the previous literature would suffer from an identification problem.²² Based on the empirical findings of Rodrik, Subramanian, and Trebbi (2004), our specification of the regression model rules out the possibility of such reverse feedbacks.

Another identification assumption is that while the size of government is affected by income levels, government size has no simultaneous effect on income levels. However, this assumption is inconsistent with our theoretical framework in that the main arguments in Section II.B are based on Keynesian assumptions, which suggest a positive effect of government spending on income level. To resolve this conceptual conflict, we follow two strategies. The first strategy is based on the assumption that government size and its fluctuation cannot affect the trend component of aggregate income. The expansionary effect of government spending is generally expected when the effective demand falls short of natural (or potential) level of income. Based on this view that government size is irrelevant to the determination of the income trend, we use the trend component of real GDP per capita as an income measure, which should rule out the reverse feedback from government size to aggregate income level.²³ However, it could be argued that government spending could change the income trend (e.g., if technological progress is endogenously determined by private investment, and government spending crowds out such investment, fiscal policy of the government could alter the income trend). As a robust test of the first strategy, we not only check the overidentifying restrictions test result, but also exclude the income variable from the IVs, and see how estimates change. Usually an arbitrary exclusion causes biases, but the exclusion of income can give us useful information in our particular setting.²⁴

The last assumption for the identification is that there is no direct relationship between the size of government and openness to trade. However, if globalization deteriorates the income inequality of an economy, a more open economy may want to neutralize this negative impact of globalization by increasing government redistribution, which in turn raises government expenditure. The empirical literature on this issue has found no decisive evidence either way (Wei and Wu, 2001). Using the OECD dataset, we examine the plausibility of this relationship by regressing the Gini coefficients of OECD countries on openness to trade. The OLS estimation result shows that the effect of trade openness on income inequality is statistically insignificant and negative, which implies that this possibility is of no empirical relevance.²⁵

In our preferred specification, equation (7) is identified using sectoral productivity difference (PRDFF), population (POP), land area (LND), income (INC), and dependency ratio (DEP). In a similar fashion, equation (8) is identified using sectoral productivity difference (PRDFF) and terms of trade shock (TOT).²⁶ The relevance and validity of these instrumental variables are statistically tested in Section III.B.

B. Data and the Sample

Using international panel data, we compute intersectoral fluctuations of labor income growth rates as follows:

\begin{matrix} {ASY}_{t} = S_{n, t} \equiv \sqrt{\frac{\sum_{j = 1}^{M} n_{j} \cdot {(Δ \ln y_{j t} - {\bar{y}}_{t}^{n})}^{2}}{1 - \sum_{j = 1}^{M} n_{j}^{2}}}, & (9) \end{matrix}

where n_j is the employment share of each sector, ${\bar{y}}_{t}^{n} \equiv \sum_{j = 1}^{M} n_{j} \cdot Δ \ln y_{jt}$ is the weighted average of labor income growth rate as shown in the previous section. The numerator inside the square root measures the deviation of sectoral labor income growth from its average. The denominator can be interpreted as an industry-concentration index. As the industries are more equal in employment, this index becomes larger. It is designed to parse out the international differences caused by differences in industry-concentration.

The data used to construct this variable is available from the STAN database published by OECD. For the computation of sectoral labor income growth, we first calculate average productivity of each industry by dividing ‘value added’ by ‘total employment.’²⁷ The labor income growth of each sector is computed using the growth rate of sectoral average labor productivity. By implicitly assuming that the labor share is stable, the growth rate of marginal labor productivity (and labor income) is equal to that of average labor productivity. It should be noted that since the growth rate of labor productivity is a nominal measure, a problem may exist if price levels are significantly different across sectors. Otherwise, intersectoral fluctuation would be a real variable because the effect of price changes on intersectoral fluctuation will be canceled out by subtracting sectoral growth rates from the average. Table 1 describes how the STAN database defines industries. This study involves 17-industry classifications: all 1-digit industries except ‘community social and personal services’ plus 2-digit industries of manufacturing sector.²⁸

Table 1.

Definition of Industries

Table 1.

Definition of Industries

Industry	Subcategory	Definition
AG00		Agriculture, hunting, forestry and fishing
MQ00		Mining and quarrying
MA00		Total manufacturing (=MA00+…+MA10)
	MA01	Food products, beverages and tobacco
	MA02	Textiles, textile products, leather and footwear
	MA03	Wood and products of wood and cork
	MA04	Pulp, paper, paper products, printing and publishing
	MA05	Chemical, rubber, plastics and fuel products
	MA06	Other non-metallic mineral product
	MA07	Basic metals and fabricated metal product
	MA08	Machinery and equipment
	MA09	Transport equipment
	MA10	Manufacturing nec; recycling
EL00		Electricity, gas and water supply
CN00		Construction
WR00		Wholesale and retail trade; restaurants and hotels (=WR01+WR02)
	WR01	Wholesale and retail trade; repairs
	WR02	Hotels and restaurants
TR00		Transport and storage and communication (=TR01+TR02)
	TR01	Transport and storage
	TR02	Post and telecommunications
FI00		Finance, insurance, real estate and business services (=FI01+FI02)
	FI01	Financial intermediation
	FI02	Real estate, renting and business activities
CS00		Community social and personal services

Table 1.

Definition of Industries

Industry	Subcategory	Definition
AG00		Agriculture, hunting, forestry and fishing
MQ00		Mining and quarrying
MA00		Total manufacturing (=MA00+…+MA10)
	MA01	Food products, beverages and tobacco
	MA02	Textiles, textile products, leather and footwear
	MA03	Wood and products of wood and cork
	MA04	Pulp, paper, paper products, printing and publishing
	MA05	Chemical, rubber, plastics and fuel products
	MA06	Other non-metallic mineral product
	MA07	Basic metals and fabricated metal product
	MA08	Machinery and equipment
	MA09	Transport equipment
	MA10	Manufacturing nec; recycling
EL00		Electricity, gas and water supply
CN00		Construction
WR00		Wholesale and retail trade; restaurants and hotels (=WR01+WR02)
	WR01	Wholesale and retail trade; repairs
	WR02	Hotels and restaurants
TR00		Transport and storage and communication (=TR01+TR02)
	TR01	Transport and storage
	TR02	Post and telecommunications
FI00		Finance, insurance, real estate and business services (=FI01+FI02)
	FI01	Financial intermediation
	FI02	Real estate, renting and business activities
CS00		Community social and personal services

Sectoral productivity difference is defined in a similar fashion. Since sectoral labor productivity level is a nominal measure, the international variations in either price level or exchange rate may exaggerate sectoral labor productivity differences. To counter this problem, we define sectoral productivity difference (PRDFF) as the weighted average of deviations in logs of sectoral labor productivity.

\begin{matrix} PRDFF \equiv \sum_{j = 1}^{M} n_{j} \cdot {(\ln y_{jt} - \ln y_{t})}^{2}, & (10) \end{matrix}

where y_jt is the average labor productivity of sector j and y_t is the aggregate labor productivity ²⁹. We use three different measures of government size in the estimation: the share of total government expenditure in GDP, the share of total government spending in GDP less that devoted to subsidies and transfers, and the share of government subsidies and transfers in GDP. These variables are constructed using the Government Financial Statistics published by the IMF.

Openness to trade is defined as the sum of exports and imports relative to GDP. This variable is available in Penn-World Table 6.1. To construct the shocks to the terms of trade, we first define the terms of trade as the ratio of the export unit value index to the import unit value index. This data is from UN dataset, and it is available from 1980 to 2001. Using the panel observations of the terms of trade, we compute its average annual percentage change over the sample period for each OECD country. Then, the terms of trade shock is defined as the absolute value of the difference between the annual percentage changes in the terms of trade and the average, which implies that we treat the percentage deviations of the terms of trade in a symmetric way.³⁰ The sources of other variables are as follows: real GDP per capita is from Penn-World Table 6.1, and the dataset in Bernanke and Gurkaynak (2001) is used for the construction of dependency ratio and population. Land area is available from World Development Indicator published by the World Bank. The full set of variables limits our empirical analysis to 15 out of 21 OECD countries available in the STAN database from 1981 to 1998. These 15 countries are then classified into five groups to assign for regional dummy variables. ³¹Summary statistics for the key variables are presented in Table 2.

Table 2.

Summary Statistics of Key Variables

Table 2.

Summary Statistics of Key Variables

Variables		Mean	Standard deviation	Minimum	Maximum	Observations
Total expenditure in percent of GDP	EXP	0.351	0.110	0.146	0.555
Expenditure less subsidies and transfers in percent of GDP	NSTEXP	0.136	0.041	0.020	0.237
Expenditure on subsidies and transfers in percent of GDP	STEXP	0.215	0.080	0.560	0.394
Intersectoral income fluctuations	ASY	0.048	0.018	0.139	0.140
Openness to trade	OPN	0.637	0.288	0.171	1.473	251
Terms of trade shock	TOT	0.030	0.039	0.000	0.277
Log of population	POP	9.859	1.158	8.319	12.507
Log of land area in square kilometers	LAND	12.740	1.882	10.317	16.037
Dependency ration	DEP	0.333	0.017	0.287	0.371
Sectoral productivity difference	PRDFF	0.275	0.157	0.112	0.820

Table 2.

Summary Statistics of Key Variables

Variables		Mean	Standard deviation	Minimum	Maximum	Observations
Total expenditure in percent of GDP	EXP	0.351	0.110	0.146	0.555
Expenditure less subsidies and transfers in percent of GDP	NSTEXP	0.136	0.041	0.020	0.237
Expenditure on subsidies and transfers in percent of GDP	STEXP	0.215	0.080	0.560	0.394
Intersectoral income fluctuations	ASY	0.048	0.018	0.139	0.140
Openness to trade	OPN	0.637	0.288	0.171	1.473	251
Terms of trade shock	TOT	0.030	0.039	0.000	0.277
Log of population	POP	9.859	1.158	8.319	12.507
Log of land area in square kilometers	LAND	12.740	1.882	10.317	16.037
Dependency ration	DEP	0.333	0.017	0.287	0.371
Sectoral productivity difference	PRDFF	0.275	0.157	0.112	0.820

IV. Estimation Results

A. Patterns of Estimates

Table 3 summarizes the estimation results, where the measure of government size is the share of government expenditure in GDP. The first four columns report the estimation results of equation (7) and the others summarize the estimation results of equation (8). In these two sets of results, the first columns report OLS estimates, the second and third columns report IV estimates, and the final columns report 3SLS estimates.³²

Table 3.

Estimation Results: Government Expenditure (EXP)

1/ Standard deviations in parenthesis.2/ Overid. test: p-value of overidentifying restriction test.3/ For ASY equation, IV₁ = using LAND, DEP, POP, INC as IVs while treating only GOV as endogenous; IV₂ = using LAND, DEP, POP, INC, PRDFF as IVs while treating both GOV and OPN as endogenous.4/ For EXP equation, IV₁ = using TOT, OPN, OPN*TOT as IVs, while treating OPN as exogenous; IV₂ = using TOT, PRDFF as IVs, while treating OPN as endogenous.5/ ASY: intersectoral fluctuation; OPN: openness to trade; TOT: terms of trade shock; POP: log of population; LAND: log of land area in square kilometer; DEP: dependency ratio; INC: log of real GDP per capita trend.6/ Year-specific and country-specific intercepts are all controlled in all estimation.

Table 3.

Estimation Results: Government Expenditure (EXP)

Dependent Variable	ASY				EXP
Estimates	OLS	IV₁	IV₂	3SLS	OLS	IV₁	IV₂	3SLS
EXP	-.030 (.018)*	-.127 (.028)***	-.121 (.036)***	-.117 (.034)***
OPN	.022 (.007)***	.039 (.008)***	.030 (.020)	.034 (.019)
OPN*TOT	.187 (.112)*	.123 (.113)	1.348 (.799)*	1.095 (.736)
TOT	-.090 (.064)	-.068 (.064)	-.685 (.405)*	-.556 (.373)*
ASY					.504 (.208)**	5.287 (2.184)**	4.023 (1.525)***	4.018 (1.524)
POP					.008 (.006)	.037 (.0168)**	.029 (.013)**	.028 (.013)
LAND					-.042 (.003)***	-.052 (.007)***	-.049 (.005)***	-.050 (.005)
DEP					.411 (.245)*	.500 (.426)	.477 (.350)	.462 (.320)
INC					.0764 (.023)***	.188 (.064)***	.159 (.048)***	.162 (.043)
Overid. test	---	.016	.926	.944	---	.074	.924	.944
Obs.	251				251

Table 3.

Estimation Results: Government Expenditure (EXP)

Dependent Variable	ASY				EXP
Estimates	OLS	IV₁	IV₂	3SLS	OLS	IV₁	IV₂	3SLS
EXP	-.030 (.018)*	-.127 (.028)***	-.121 (.036)***	-.117 (.034)***
OPN	.022 (.007)***	.039 (.008)***	.030 (.020)	.034 (.019)
OPN*TOT	.187 (.112)*	.123 (.113)	1.348 (.799)*	1.095 (.736)
TOT	-.090 (.064)	-.068 (.064)	-.685 (.405)*	-.556 (.373)*
ASY					.504 (.208)**	5.287 (2.184)**	4.023 (1.525)***	4.018 (1.524)
POP					.008 (.006)	.037 (.0168)**	.029 (.013)**	.028 (.013)
LAND					-.042 (.003)***	-.052 (.007)***	-.049 (.005)***	-.050 (.005)
DEP					.411 (.245)*	.500 (.426)	.477 (.350)	.462 (.320)
INC					.0764 (.023)***	.188 (.064)***	.159 (.048)***	.162 (.043)
Overid. test	---	.016	.926	.944	---	.074	.924	.944
Obs.	251				251

Determinants of intersectoral income fluctuation: equation (7)

Not surprisingly, the first column of the ASY equation shows that the OLS estimate of total expenditure (EXP) is a small negative number of -0.03, statistically insignificant at a 5 percent level. We first correct for the endogeneity of EXP by using the set of IVs: LAND, DEP, POP, INC. The corrected estimate of EXP turns out -0.13, a greater estimate with statistical significance (see the IV₁ column). We are, however, concerned with the low overidentifying restrictions test result of p-value=0.02. This result suggests that openness to trade should have been treated as an endogenous variable as our theory section shows. In the third column (IV2), we thus treat EXP, OPN and OPN⋅TOT as endogenous and use an additional IV of productivity difference (PRDFF) as well as the aforementioned IVs to control the endogeneity of openness to trade. The resulting estimate of EXP is −0.12 with a high statistical significance. The validity of IVs is also supported by the high overidentifying restrictions test result of p-value=0.93, implying the results using IV2 are most reliable.

To see the importance of government expenditure in stabilizing intersectoral income fluctuation, we examine how much of the variations in intersectoral fluctuation can be explained by the variations in government size using the estimates based on IV2. The sample standard deviations of the government size and intersectoral fluctuation are 0.110 and 0.018, respectively. The estimate predicts that the changes in the government size by its sample standard deviation will cause the changes in intersectoral fluctuation by about 74 percent of its sample standard deviation.³⁶ This simple computation roughly shows that about 74 percent of the sample variations in intersectoral income fluctuations can be explained by the sample variations in government expenditure.

The estimation of equation (7) provides another interesting result. As we predicted in Section II.C, economic uncertainty measured by intersectoral fluctuation of labor income growth rates becomes larger as an economy is more open to international trade. While the partial effect of openness to trade on intersectoral fluctuation is smaller than that of government expenditure in absolute value, its effect is still nontrivial. The partial effect of openness to trade on intersectoral fluctuation depends on the terms of trade shocks that an economy faces: ∂ASY/∂OPN =.03 +1.35 ⋅TOT. Evaluating this effect at the sample mean of terms of trade shock (0.03), we can see that the changes in the openness to trade by its sample standard deviations (0.288) can cause a change in intersectoral fluctuation by about 113 percent of its sample standard deviations (0.018).³⁷ While our empirical specification differs from that of Rodrik (1998), our finding confirms one of his main hypotheses: a more open economy faces higher economic uncertainty.

In Section II.C, we show that external shocks are likely to decrease intersectoral fluctuation in less open economies while they can increase sector-specific income risks in more open economies. The estimation provides a consistent result with our theoretical prediction. According to our estimation result, the partial effect of terms of trade shock is ∂ASY/∂TOT =−0.69 +1.35 ⋅OPN.³⁸ Using this partial effect, we can compute a cutoff value of openness to trade, open^C. Since open^C =0.69/1.35 =0.51, the estimation result implies that when the openness to trade of an economy is higher (lower) than 50 percent, an increase in the terms of trade shock raises (reduces) intersectoral fluctuation.

Determinants of government size: equation (8)

In the estimation of the government equation (8), we find a similar pattern as in that of the ASY equation (7). The first column under the EXP section shows that the estimated coefficient of ASY by OLS is a small positive but statistically significant number of 0.50. We first correct for the endogeneity of ASY by using the set of IVs: TOT, OPN, and OPN*TOT treating OPN as exogenous. The corrected estimate of ASY turns out 5.29, a much greater estimate with statistical significance (see the IV1 column). This result is, however, overshadowed by the low overidentifying restrictions test result of p-value=0.07. Put differently, it suggests that OPN is again endogenous. To deal with this endogeneity, we thus use TOT and PRDFF as another set of IVs (see the third column, IV2). The estimate of ASY is now 4.02 with a high statistical significance, and the validity of IVs is supported by the high overidentifying restrictions test result of p-value=0.92.

The estimation results support our theoretical prediction: an economy facing higher economic uncertainty has a larger government. The estimate shows that a country with its intersectoral income fluctuation one standard deviation (0.018) higher than the sample average has a government 7.4 percent larger than the average, which amounts to 70 percent of the sample standard deviation of government expenditure.

It is also worth noting all the other estimates reported in EXP column. First, the dependency ratio has a positive effect on the size of government although it is found to be statistically insignificant. The regression result confirms Wagner’s law, which states that the share of government expenditure increases with income. Specifically, our estimate of 0.16 means that when we evaluate this at the sample average of government expenditure (0.35), the elasticity of the size of government to income is 1.45.³⁹Lastly, two measures of country size are found to have opposite effects on government expenditure. Given land area, the economy with more population has larger government expenditure while the economy with broader territories has lower government expenditure for a given population. This finding that an economy that is larger in size of territories but smaller in population has a smaller government is also confirmed in the regression that includes population density instead of population and land area separately.⁴⁰ In this case, the congestion (population density) may deserve our attention as one of the factors that explain government expenditure.

Accounting for differences among estimates

At this point, we can explain the differences between OLS and IV estimates.⁴¹⁴² Since endogenous variables exert opposite influences on each other, the simultaneous equation bias will push the estimated coefficient toward zero for OLS estimation.⁴³ In the case of openness to trade, its partial effect on economic uncertainty is much larger in IV2 estimation compared to OLS and IV1 estimation, which treat OPN as an exogenous variable by ignoring the reverse negative feedback from intersectoral fluctuation to OPN (Table 6). Given the implied validity of IVs, we perform 3SLS estimation for efficiency improvement. As expected, the 3SLS columns of Table 3 show similar estimates with somewhat higher statistical significance, further evidence on the validity of our IV estimation.

Table 4.

Estimation Results: Expenditure Less Subsidies and Transfers (NSTEXP)

Notes: See the notes in Table 3.

Table 4.

Estimation Results: Expenditure Less Subsidies and Transfers (NSTEXP)

Dependent Variable	ASY				NSTEXP
Estimates	OLS	IV1	IV2	3SLS	OLS	IV1	IV2	3SLS
NSTEXP	-.118 (.035)***	-.193 (.046)***	-.201 (.067)***	-.190 (.062)
OPN	.026 (.007)***	.032 (.007)***	.017 (.020)	.020 (.019)
OPN*TOT	.185 (.109)*	.172 (.105)*	1.848 (.844)**	1.607 (.768)
TOT	-.088 (.063)	-.084 (.060)	-.931 (.430)*	-.805 (.391)
ASY					.005 (.091)	1.865 (.882)**	.832 (.517)*	.849 (.516)
POP					-.003 (.003)	.008 (.007)	.002 (.004)**	.001 (.004)
LAND					-.023 (.001)***	-.027 (.003)***	-.025 (.002)***	-.025 (.002)
DEP					.502 (.107)***	.537 (.172)***	.520 (.119)***	.529 (.116)
INC					.050 (.010)***	.093 (.026)***	.069 (.016)***	.071 (.015)
Overid. test	---	.001	.922	.800	---	.270	.589	.800
Obs.	251				251

Notes: See the notes in Table 3.

Table 4.

Estimation Results: Expenditure Less Subsidies and Transfers (NSTEXP)

Dependent Variable	ASY				NSTEXP
Estimates	OLS	IV1	IV2	3SLS	OLS	IV1	IV2	3SLS
NSTEXP	-.118 (.035)***	-.193 (.046)***	-.201 (.067)***	-.190 (.062)
OPN	.026 (.007)***	.032 (.007)***	.017 (.020)	.020 (.019)
OPN*TOT	.185 (.109)*	.172 (.105)*	1.848 (.844)**	1.607 (.768)
TOT	-.088 (.063)	-.084 (.060)	-.931 (.430)*	-.805 (.391)
ASY					.005 (.091)	1.865 (.882)**	.832 (.517)*	.849 (.516)
POP					-.003 (.003)	.008 (.007)	.002 (.004)**	.001 (.004)
LAND					-.023 (.001)***	-.027 (.003)***	-.025 (.002)***	-.025 (.002)
DEP					.502 (.107)***	.537 (.172)***	.520 (.119)***	.529 (.116)
INC					.050 (.010)***	.093 (.026)***	.069 (.016)***	.071 (.015)
Overid. test	---	.001	.922	.800	---	.270	.589	.800
Obs.	251				251

Notes: See the notes in Table 3.

Table 5.

Estimation Results: Expenditure on Subsidies and Transfers (STEXP)

Notes: See the notes in Table 3.

Table 5.

Estimation Results: Expenditure on Subsidies and Transfers (STEXP)

Dependent Variable	ASY				STEXP
Estimates	OLS	IV1	IV2	3SLS	OLS	IV1	IV2	3SLS
STEXP	.001 (.025)	-.300 (.074)***	-.271 (.087)***	-.277 (.084)
OPN	.017 (.007)**	.045 (.011)***	.045 (.024)*	.051 (.023)
OPN*TOT	.207 (.112)*	.065 (.139)*	.759 (.890)	.421 (.861)
TOT	-.096 (.064)	-.049 (.078)	-.396 (.449)	-.22 (.434)
ASY					.499 (.174)***	3.422 (1.499)**	3.819 (1.217)***	3.221 (1.212)
POP					.012 (.005)**	.029 (.012)**	.028 (.0100)***	.028 (.010)
LAND					-.019 (.003)***	-.025 (.005)***	-.025 (.004)***	-.025 (.004)
DEP					-.092 (.205)	-.037 (.292)	-.0413 (.279)	-.100 (.272)
INC					.027 (.019)	.095 (.044)***	.090 (.038)**	.087 (.035)
Overid test	---	.196	.546	.920	---	.067	.913	.920
Obs.	251				251

Notes: See the notes in Table 3.

Table 5.

Estimation Results: Expenditure on Subsidies and Transfers (STEXP)

Dependent Variable	ASY				STEXP
Estimates	OLS	IV1	IV2	3SLS	OLS	IV1	IV2	3SLS
STEXP	.001 (.025)	-.300 (.074)***	-.271 (.087)***	-.277 (.084)
OPN	.017 (.007)**	.045 (.011)***	.045 (.024)*	.051 (.023)
OPN*TOT	.207 (.112)*	.065 (.139)*	.759 (.890)	.421 (.861)
TOT	-.096 (.064)	-.049 (.078)	-.396 (.449)	-.22 (.434)
ASY					.499 (.174)***	3.422 (1.499)**	3.819 (1.217)***	3.221 (1.212)
POP					.012 (.005)**	.029 (.012)**	.028 (.0100)***	.028 (.010)
LAND					-.019 (.003)***	-.025 (.005)***	-.025 (.004)***	-.025 (.004)
DEP					-.092 (.205)	-.037 (.292)	-.0413 (.279)	-.100 (.272)
INC					.027 (.019)	.095 (.044)***	.090 (.038)**	.087 (.035)
Overid test	---	.196	.546	.920	---	.067	.913	.920
Obs.	251				251

Notes: See the notes in Table 3.

Table 6.

Government Size Effect on Uncertainty: Equation (7)

^{^1/}IV₁ and IV₂ are defined as in the note 3 of Table 3.

^{^2/}INC is excluded from the list of instruments variables in the note 3 of Table 3.

^{^3/}Partial effect of openness is evaluated at the sample average of TOT (.03).

Table 6.

Government Size Effect on Uncertainty: Equation (7)

Dependent Variable	Estimation Method	EXP		NSTEXP		STEXP
Dependent Variable	Estimation Method	EXP	OPN^3/	NSTEXP	OPN^3/	STEXP	OPN^3/
		INC included in IVs
ASY^1/	OLS	-0.030 (.018)	0.028 (.007)	-0.118 (.035)	0.032 (.007)	0.001 (.025)	0.023 (.007)
	IV₁	-0.127 (.028)	0.043 (.008)	-0.193 (.046)	-0.037 (.007)	-0.300 (.074)	0.047 (.010)
	IV₂	-0.121 (.036)	0.070 (.013)	-0.201 (.067)	0.071 (.015)	-0.271 (.087)	0.067 (.013)
		INC excluded from IVs
ASY^2/	OLS	-0.030 (.018)	0.028 (.007)	-0.118 (.035)	0.032 (.007)	0.001 (.025)	0.023 (.007)
	IV₁	-0.116 (.029)	0.041 (.008)	-0.169 (.048)	0.035 (.007)	-0.279 (.073)	0.046 (.009)
	IV₂	-0.120 (.036)	0.069 (.014)	-0.209 (.074)	0.074 (.018)	-0.277 (.083)	0.062 (.014)

^{^1/}IV₁ and IV₂ are defined as in the note 3 of Table 3.

^{^2/}INC is excluded from the list of instruments variables in the note 3 of Table 3.

^{^3/}Partial effect of openness is evaluated at the sample average of TOT (.03).

Table 6.

Government Size Effect on Uncertainty: Equation (7)

Dependent Variable	Estimation Method	EXP		NSTEXP		STEXP
Dependent Variable	Estimation Method	EXP	OPN^3/	NSTEXP	OPN^3/	STEXP	OPN^3/
		INC included in IVs
ASY^1/	OLS	-0.030 (.018)	0.028 (.007)	-0.118 (.035)	0.032 (.007)	0.001 (.025)	0.023 (.007)
	IV₁	-0.127 (.028)	0.043 (.008)	-0.193 (.046)	-0.037 (.007)	-0.300 (.074)	0.047 (.010)
	IV₂	-0.121 (.036)	0.070 (.013)	-0.201 (.067)	0.071 (.015)	-0.271 (.087)	0.067 (.013)
		INC excluded from IVs
ASY^2/	OLS	-0.030 (.018)	0.028 (.007)	-0.118 (.035)	0.032 (.007)	0.001 (.025)	0.023 (.007)
	IV₁	-0.116 (.029)	0.041 (.008)	-0.169 (.048)	0.035 (.007)	-0.279 (.073)	0.046 (.009)
	IV₂	-0.120 (.036)	0.069 (.014)	-0.209 (.074)	0.074 (.018)	-0.277 (.083)	0.062 (.014)

^{^1/}IV₁ and IV₂ are defined as in the note 3 of Table 3.

^{^2/}INC is excluded from the list of instruments variables in the note 3 of Table 3.

^{^3/}Partial effect of openness is evaluated at the sample average of TOT (.03).

B. Further Results

Using other measures of government size

Tables 4 and 5 summarize the estimation results where government size is measured by expenditure less subsidies and transfers in percent of GDP (NSTEXP) or expenditure on subsidies and transfers in percent of GDP (STEXP). It should be noted that by definition, the sum of these two measures is equal to total government expenditure in this empirical study. For this reason, the estimates for equation (8) reported in Table 3 are close to the sum of the estimates reported in Tables 4 and 5.

While the estimation results are similar to those in Table 3, we can see a notable distinction in Table 4. While NSTEXP is effective in reducing intersectoral fluctuation, it is less sensitive to the changes in intersectoral fluctuation than EXP or STEXP. The coefficient on intersectoral fluctuation in Table 4 is smaller than that of Tables 3 and 5. This implies that government resorts to redistributive measures when it deals with sector-specific income risks even though expenditure less subsidies and transfers is also an effective option for this purpose. This finding is consistent with other studies (Gali, 1994; Sachs and Sala-i-Martin, 1992), which point out that government spending is stabilizing even when it is not designed for a stabilization purpose.

In principle, the redistributive measures of government hardly affect intersectoral fluctuation in ‘gross’ income if the demand side is completely passive in the determination of the equilibrium income. However, Table 5 shows that government subsidies and transfers reduce intersectoral fluctuation. There are two general reasons why we have a stabilization effect of the redistributive measures. First, our sectoral value added data from STAN database includes government subsidies and some taxes in it. For this reason, the redistributive measures may reduce intersectoral income fluctuations. The second possibility is that consumers allocate spending of the transferred income on the final goods in a proportional way. In this case, the transfers to consumers and government’s direct spending would have qualitatively equivalent effect on intersectoral income fluctuations. As mentioned before, we can see from Tables 4 and 5 that the response of STEXP to intersectoral fluctuation (3.82 in IV2 column) is much greater than that of NSTEXP (0.83). This implies that government does not rely on its direct spending for the stabilization of intersectoral income fluctuations although expenditure less subsidies and transfers is almost as effective as government subsidies and transfers for this purpose. This tendency may be attributable to the fact that redistributive measures are normally better targeted, and thereby more efficient in directing resources from temporarily good sectors to temporarily bad sectors. In addition, if both measures have qualitatively similar effects on income uncertainty, then individuals would prefer redistributive measures, which presumably offer more consumption choices to the beneficiaries than government direct spending.

Another miscellaneous finding is that STEXP are less elastic with respect to income changes than NSTEXP. From Table 3, we show that the elasticity of total government expenditure is 1.45. The corresponding figures for NSTEXP and STEXP are 1.51 and 1.41, respectively. However, it should be noted that STEXP are on average larger than NSTEXP, and thus their impact on government expenditure is greater even if they are less elastic.⁴⁴ In the overall elasticity of 1.45, 59 percent of the response comes from increases in STEXP and the remaining 41 percent comes from increases in NSTEXP. In the statistical point of view, the choice of government size makes little differences in the results of overidentification test. As reported in Tables 4 and 5, we cannot reject the overidentifying restrictions at a conventional significance level.

Checking the validity of INC as IV

As argued in Section II.D, the use of income trend may not perfectly handle the potential endogeneity of the income variable. As a robustness test, we re-estimate equations (7) and (8) with INC excluded from equation (8). Tables 6 and 7 summarize the estimation results of our key endogenous variables of interest. First, comparing the top panel (using INC as IV) with the bottom panel of Table 6, we find that key estimates in equation (7) are hardly affected by the exclusion of INC from the identifying restrictions. This lends support to our use of the INC variable for controlling income trend. Second, reading Table 7 in the same way as Table 6, we see that while some estimated coefficients of equation (8) change with the exclusion of INC, the estimated impact of ASY on three measures of government size—our primary interest in this paper—mostly remains meaningful and significant.

Table 7.

Uncertainty Effect on Government Size: Equation (8)

^{^1/}IV₁ and IV₂ are defined as in the note 4 of Table 3.

^{^2/}INC is included as a regressor in equation (8).

^{^3/}INC is excluded from equation (8).

Table 7.

Uncertainty Effect on Government Size: Equation (8)

Dependent Variable	Estimation Method ^1/	ASY^2/		ASY^3/
Dependent Variable	Estimation Method ^1/	INC included		INC excluded
EXP	OLS	0.504	(0.208)	0.358	(0.208)
	IV₁	5.287	(2.184)	3.671	(1.488)
	IV₂	4.023	(1.525)	3.102	(1.226)
NSTEXP	OLS	0.005	(0.091)	-0.089	(0.093)
	IV₁	1.865	(0.882)	1.034	(0.587)
	IV₂	0.832	(0.517)	0.399	(0.438)
STEXP	OLS	0.499	(0.174)	0.448	(0.171)
	IV₁	3.422	(1.499)	2.637	(1.101)
	IV₂	3.191	(1.217)	2.703	(1.007)

^{^1/}IV₁ and IV₂ are defined as in the note 4 of Table 3.

^{^2/}INC is included as a regressor in equation (8).

^{^3/}INC is excluded from equation (8).

Table 7.

Uncertainty Effect on Government Size: Equation (8)

Dependent Variable	Estimation Method ^1/	ASY^2/		ASY^3/
Dependent Variable	Estimation Method ^1/	INC included		INC excluded
EXP	OLS	0.504	(0.208)	0.358	(0.208)
	IV₁	5.287	(2.184)	3.671	(1.488)
	IV₂	4.023	(1.525)	3.102	(1.226)
NSTEXP	OLS	0.005	(0.091)	-0.089	(0.093)
	IV₁	1.865	(0.882)	1.034	(0.587)
	IV₂	0.832	(0.517)	0.399	(0.438)
STEXP	OLS	0.499	(0.174)	0.448	(0.171)
	IV₁	3.422	(1.499)	2.637	(1.101)
	IV₂	3.191	(1.217)	2.703	(1.007)

^{^1/}IV₁ and IV₂ are defined as in the note 4 of Table 3.

^{^2/}INC is included as a regressor in equation (8).

^{^3/}INC is excluded from equation (8).

V. Summary and Conculsions

While there has been an extensive empirical literature on the stabilization effect of government spending on income, no existing paper has examined the interaction between economic uncertainty and government size as the stabilization effort of a government. This paper addresses this issue within a Keynesian framework utilizing the intersectoral income fluctuations as a new measure of economic uncertainty.

Our empirical model allows for the interaction of government size and economic uncertainty in the open economy context. Taking into account the interaction in accordance with our simple models, we obtained the following main results. As Rodrik (1998) hypothesized, this study finds that an economy with high intersectoral income fluctuations will have a large government, but at the same time, the size of government has a substantial effect on the stabilization of intersectoral income fluctuations. Examining different measures of government size, we also find that expenditure less subsidies and transfers is not an active policy option for stabilization, even though it is almost as effective as the other component of government expenditure in reducing uncertainty.

In the open economy context, we also obtained another interesting result that openness to trade and external shocks are important determinants of economic uncertainty. In open economies, sector-specific shocks cannot be diffused into the whole economy since the domestic price of the final goods of each sector is fixed at the international price. For this reason, more open economies face more sector-specific income risks and the impact of openness to trade on intersectoral income fluctuations further rises as an economy is exposed to more intense external shocks. This study also finds that the effect of terms of trade shock on intersectoral income fluctuations depends on the openness of an economy. When the sum of export and import relative to GDP is larger (smaller) than 50 percent, terms of trade shock increases (decreases) intersectoral fluctuation.

APPENDIX I. PROOF OF RESULTS

Proof of Result 1:

Proof: $λ_{i} \equiv \frac{G_{i}}{N_{i} . y_{i}} = \frac{1}{y_{i}} . \frac{α_{i}}{N_{i}} . G = \frac{λ}{y_{i}} . \frac{α_{i}}{n_{i}} . y = λ$ since $α_{i} \equiv \frac{G_{i}}{G}$ and $α_{i} = \frac{y_{i}}{y} . n_{i} \equiv γ_{i} .$

Proof of Result 2:

Proof: Since the proof about expectation is straightforward, we skip it. The variance conditional on t is:

\begin{matrix} var (Δ \ln y_{it} | t) = E [Δ \ln y_{it} - E {(Δ \ln y_{it} | t)}^{2} | t] \\ = {(1 - λ)}^{2} \cdot E [{(ε_{i t} - E (ε_{it} | t))}^{2} | t] = {(1 - λ)}^{2} \cdot var (ε_{it} | t) = {(1 - λ)}^{2} \cdot σ_{ε}^{2} \cdot \end{matrix}

Proof of Result 3:

Proof: we prove the unbiasedness of

{\bar{y}}_{t}^{n}

and

s_{n, t}^{2}

. First, we prove the unbiasedness of

{\bar{y}}_{t}^{γ}

and

s_{γ, t}^{2}

. First, we prove the unbiasedness of

{\bar{y}}_{t}^{n}

\begin{array}{l} E ({\bar{y}}_{t}^{n} | t) = E (\sum_{j = 1}^{M} n_{j} \cdot Δ \ln y_{jt} | t) = \sum_{j = 1}^{M} n_{j} \cdot E (Δ \ln y_{jt} | t) = \sum_{j = 1}^{M} n_{j} \cdot [θ + (1 - λ) \cdot μ_{t}] = θ + (1 - λ) \cdot μ_{t} \\ = E (Δ \ln y_{it} | t) \end{array}

The unbiasedness of

s_{n, t}^{2}

means that

E (s_{n, t}^{2} | t) = var (Δ \ln y_{it} | t) = {(1 - λ)}^{2} \cdot σ_{ε}^{2} \cdot

\begin{array}{l} E (s_{n, t}^{2} | t) = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot E [\sum_{j = 1}^{M} n_{j} \cdot {[(Δ \ln y_{jt} - E ({\bar{y}}_{t}^{n} | t)) - ({\bar{y}}_{t}^{n} - E ({\bar{y}}_{t}^{n} | t))]}^{2} | t] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot E [\sum_{j = 1}^{M} n_{j} \cdot {(Δ \ln y_{jt} - E ({\bar{y}}_{t}^{n} | t))}^{2} \\ - 2 \cdot \sum_{j = 1}^{M} n_{j} \cdot (Δ \ln y_{jt} - E ({\bar{y}}_{t}^{n} | t)) \cdot ({\bar{y}}_{t}^{n} - E ({\bar{y}}_{t}^{n} | t)) + {({\bar{y}}_{t}^{n} - E ({\bar{y}}_{t}^{n} | t))}^{2} | t] . \end{array}

Note that

E ({\bar{y}}_{t}^{n} | t) = E (Δ \ln y_{it} | t) .

\begin{array}{l} E (s_{n, t}^{2} | t) = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot {E [\sum_{j = 1}^{M} n_{j} \cdot {(Δ \ln y_{jt} - E (Δ \ln y_{jt} | t))}^{2} | t] \\ - 2 \cdot E [({\bar{y}}_{t}^{n} - E ({\bar{y}}_{t}^{n} | t)) \cdot \sum_{j = 1}^{M} n_{j} \cdot (Δ \ln y_{it} - E ({\bar{y}}_{t}^{n} | t)) | t] + E [{({\bar{y}}_{t}^{n} - E ({\bar{y}}_{t}^{n} | t))}^{2} | t]} \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot [\sum_{j = 1}^{M} n_{j} \cdot var (Δ \ln y_{jt} | t) - E [{({\bar{y}}_{t}^{n} - Ε ({\bar{y}}_{t}^{n} | t))}^{2} | t]] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot [{(1 - λ)}^{2} \cdot σ_{ε}^{2} - var ({\bar{y}}_{t}^{n} | t)] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot [{(1 - λ)}^{2} \cdot σ_{ε}^{2} - var (\sum_{j = 1}^{M} n_{j} \cdot [θ + (1 - λ) \cdot ε_{jt}] | t)] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot [{(1 - λ)}^{2} \cdot σ_{ε}^{2} \cdot (1 - \sum_{j = 1}^{M} n_{j}^{2})] = {(1 - λ)}^{2} \cdot σ_{ε}^{2} \end{array}

Proof of Result 4:

Proof: Since the proof of variance is almost identical to the proof in ^{Result 2}, we skip it. We prove here the unbiasedness of

{\hat{σ}}_{n}^{2} .

. The same steps apply to the proof of the unbiasedness of

{\hat{σ}}_{γ}^{2} .

Since

E ({\hat{σ}}_{n}^{2}) = \frac{1}{T} \cdot \sum_{t = 1}^{T} E (s_{n, t}^{2}) = E (s_{n, t}^{2}),

we show

E (s_{n, t}^{2}) = {(1 - λ)}^{2} \cdot σ^{2} .

\begin{array}{l} E (s_{n, t}^{2}) = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot E [\sum_{j = 1}^{M} n_{j} \cdot {(Δ \ln y_{jt} - {\bar{y}}_{t}^{n})}^{2}] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot E [\sum_{j = 1}^{M} n_{j} \cdot {[(Δ \ln y_{jt} - θ) - ({\bar{y}}_{t}^{n} - θ)]}^{2}] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot [\sum_{j = 1}^{M} n_{j} \cdot E {(Δ \ln y_{jt} - θ)}^{2} - E {({\bar{y}}_{t}^{n} - θ)}^{2}] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot [\sum_{j = 1}^{M} n_{j} \cdot var (Δ \ln y_{jt}) - var ({\bar{y}}_{t}^{n})] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot [var (Δ \ln y_{it}) - var (θ + (1 + λ) \cdot \sum_{j = 1}^{M} n_{j} \cdot ε_{jt})] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot [var (Δ \ln y_{it}) - {(1 - λ)}^{2} \cdot var (\sum_{j = 1}^{M} n_{j} \cdot ε_{jt})] \\ = \frac{1}{1 - \sum_{j = 1}^{M} n_{j}^{2}} \cdot [{(1 - λ)}^{2} \cdot σ^{2} - {(1 - λ)}^{2} \cdot {\sum_{j = 1}^{M} n_{j}^{2} \cdot σ}^{2}] \\ = {(1 - λ)}^{2} \cdot σ^{2} \end{array}

APPENDIX II. THE EQUILIBRIUM OF THE OPEN ECONOMY MODEL

The equilibrium of the economy with trade barrier can be summarized as follows.

p^{R} = \frac{[1 - α ∙ (1 - γ)] ∙ {(\frac{p_{2}^{W}}{p_{Z}})}^{\frac{γ}{1 - γ}} ∙ γ^{\frac{γ}{1 - γ}} ∙ A_{1}^{\frac{1}{1 - γ}} ∙ N_{1}}{(1 - β) . {(\frac{p_{2}^{W}}{p_{Z}})}^{\frac{β}{1 - β}} ∙ β^{\frac{β}{1 - β}} ∙ A_{2}^{\frac{1}{1 - β}} ∙ N_{2}}

Z_{1}^{R} = {(p^{R})}^{\frac{1}{γ - 1}} {(\frac{p_{2}^{W} ∙ γ ∙ A_{1}}{p_{z}})}^{\frac{1}{1 - γ}} ∙ N_{1} and Z_{2}^{R} = {(p^{R})}^{\frac{1}{γ - 1}} {(\frac{p_{2}^{W} ∙ β ∙ A_{2}}{p_{z}})}^{\frac{1}{1 - β}} ∙ N_{2}

w_{1}^{R} = (1 - γ) ∙ A_{1} ∙ {(Z_{1}^{R})}^{γ} ∙ N_{1}^{- γ} and w_{2}^{R} = p^{R} ∙ (1 - β) ∙ A_{2} ∙ {(Z_{2}^{R})}^{β} ∙ N_{2}^{- β}

T^{R} = \frac{2 ∙ [\frac{p^{R} ∙ p_{I} ∙ (Z_{1}^{R} + Z_{2}^{R})}{p_{2}^{W}}]}{N_{1} ∙ w_{1}^{R} + N_{2} ∙ w_{2}^{R}}

The superscript R implies the equilibrium values are for the economy R. p is the domestic price of X₂, $p_{2}^{W}$ is the international price of X_2, and p_Z is the international price of the intermediate good. A’s are the productivity level of each industry, N’s are the number of each type of workers, and Z’s are the intermediate goods consumed by each sector. w’s are labor income of each type of workers. T is trade openness, which is defined as the sum of export and import divided by value added.

The equilibrium of the economy with free trade policy can be summarized as follows.

p^{F} = \frac{p_{2}^{W}}{p_{1}^{W}}; Z_{1}^{F} = {(\frac{γ ∙ A_{1} ∙ p_{1}^{W}}{p_{z}})}^{\frac{1}{1 - γ}} ∙ N_{1} and Z_{2}^{F} = {(\frac{β ∙ A_{2} ∙ p_{2}^{W}}{p_{z}})}^{\frac{1}{1 - β}} ∙ N_{2}

w_{1}^{F} = (1 - γ) . A_{1}^{\frac{1}{1 - γ}} . {(\frac{γ . p_{1}^{W}}{p_{z}})}^{\frac{γ}{1 - γ}} and w_{2}^{F} = (1 - β) ∙ A_{2}^{\frac{1}{1 - β}} ∙ {(\frac{β ∙ p_{2}^{W}}{p_{z}})}^{\frac{β}{1 - β}} ∙ (\frac{p_{2}^{W}}{p_{1}^{W}})

S_{1}^{F} = A_{1} ∙ {(Z_{1}^{F})}^{γ} ∙ N_{1}^{1 - γ} and S_{2}^{F} = A_{2} ∙ {(Z_{2}^{F})}^{β} ∙ N_{2}^{1 - β}

D_{1}^{F} = α ∙ [N_{1} ∙ w_{1}^{F} + N_{2} . w_{2}^{F}] and D_{2}^{F} = (\frac{p_{1}^{W}}{p_{2}^{W}}) ∙ (1 - α) ∙ [N_{1} ∙ w_{1}^{F} + N_{2} ∙ w_{2}^{F}]

T^{F} = \frac{[| S_{1}^{F} - D_{1}^{F} | + (\frac{p_{2}^{W}}{p_{1}^{W}}) ∙ | S_{2}^{F} - D_{2}^{F} | + (\frac{p_{Z}}{p_{1}^{W}}) ∙ (Z_{1}^{F} + Z_{2}^{F})]}{N_{1} ∙ w_{1}^{F} + N_{2} ∙ w_{2}^{F}}

The superscript F implies the equilibrium values are for the economy F. Ss and Ds are domestic productions and demands, respectively. Therefore, the absolute value of the difference between S and D is the domestic value of final goods trade. The definitions of the rest of the variables are the same as before.

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“We are grateful to Robert Barsky, Susanto Basu, Junko Koeda, John Laitner, Gary Saxonhouse, Alonso Segura, John Thornton, and participants in several seminars for helpful comments and suggestions.”

In public economics, see Musgrave (1959) stressing stabilization as one of the roles the government should play.

For the imperfect risk sharing in the presence of asymmetric income shocks, see Asdrubali, Sorensen, and Yosha (1996). Cochrane (1991) also shows imperfect consumption insurance in his empirical research.

These studies measure the size of government based on various fiscal data, including government expenditure, tax revenue, and total transfer in percent of GDP.

Region-specific fixed effects and year-specific effects are often correlated with the government size and uncertainty of an economy, which makes statistical inference on the relationship between government size and uncertainty difficult in the previous cross-sectional studies that use the variance of GDP growth rates.

A shock to nominal exchange rate would be one of the most intuitive examples, which will affect export and import sectors in opposite directions while its total effect on aggregate income would be mitigated through aggregating these two sectors.

As in a simple Keynesian model, we assume the presence of underutilized factors of production. This approach is similar to Rodrik (1998), which relies on the variance-covariance structure of the components of GDP for each country.

The assumption on the covariance structure does not make any difference to the partial relationship between government size and the intensity of intersectoral fluctuation. It was adopted for clarity of exposition.

For example, the government spends x percent of the total government spending to sector i if sector i’s steady state income is x percent of the total steady state income of the economy. However, we can still have qualitatively same results with much weaker assumption that the proportion of government spending allocated to sector i, $\frac{G_{i}}{G}$ is constant over time.

For analytical convenience, we assume that the number of workers in each sector is constant over time.

The mathematical proof is in Appendix I.

There are many studies on the effects of government spending on real activities. In a macroeconomic perspective, distortionary taxes or government-expenditure programs are often pointed out as a primary source of real costs of government. For detail, see Barro (1990, 1991) among others.

The second-order condition suggests that $- Γ ″ (λ^{*}) > - 2 \cdot B \cdot σ_{ε}^{2} ⁄ A$ should hold. This condition implies that the real marginal benefit of government spending −Γ(⋅) does not decrease too fast.

Due to the immobility of labor, factor price (wage) equalization does not hold in this model.

The equilibrium of economies R and F is described in Appendix II.

Actually, the condition that we propose in ^{Result 5} is not the only case that supports the result. Unless the magnitude of shocks is extremely different and/or the intermediate good shares are drastically different in the two sectors, we will have a positive relationship between openness to trade and intersectoral fluctuation.

For most of oil-importing countries, oil price shocks are a good example of this type of shocks.

The demand for infant industry protection is greater especially when labor is immobile due to technical reasons.

Lagged measure of openness is often used to resolve the endogeneity problem of openness. However, as Rodrik (1998) mentioned, it does not fully get around this problem.

The first stage regression shows that sectoral productivity difference has a negative effect on openness to trade.

Rodriguez and Rodrik (2001) provide an excellent survey on this issue while maintaining a critical view.

Rodrik et al (2004) control for the quality of institutions using IVs that are recently developed by Acemoglu et al (2001). Their results indicate that the quality of institutions “trumps” everything else. In addition to the insignificance of trade, conventional measures of geography have, at best, weak direct effects on income once institutions are controlled for, although geographic factors have a strong indirect effect by influencing the quality of institutions.

The trend component of log of real per capita GDP is computed using Hodrick-Prescott Filter with a smoothing parameter of 400.

This exclusion provides an opportunity to check the endogeneity of INC and other useful information. First, if INC is endogenous, the 2SLS estimation of ^{equation (7)} with this exclusion will produce different but unbiased estimates. If estimates do not change much, INC would not be endogenous at least in our sample. Second, exclusion of a relevant variable causes misspecification problems in ^{equation (8)}, but at least the primary variable of interest, ASY, does not seem to be correlated with INC. So we can still obtain useful information with the exclusion while checking its validity.

The Gini coefficients are from Government Financial Statistics (2001, IMF). The OLS regression uses 125 observations, and it controls year-specific and region-specific effects. A negative coefficient implies that more open economies tend to have more equitable income distribution.

The argument made for the identification of ^{equations (7)} and ⁽⁸⁾ implicitly introduces the following equation into the system of equations: OPN_it = c_j + y_t +γ₁·ASY_it + γ₂·POP_it + γ₃·LND_it + γ₄·INC_it + γ₅·PRDFF_it +υ_it where υ is error term.

All other measures of employment and output in STAN dataset produce qualitatively the same empirical results, while ‘total employment’ and ‘value added at current price’ provide more observations than any other measure does.

Community social and personal services, which are a part of government expenditure, are excluded in the calculation of intersectoral income fluctuation. The study also tested the sensitivity of the empirical findings with respect to the inclusion or exclusion of ‘community social and personal services’ and ‘mining and quarrying’. There were no significant differences in the empirical results.

We can reflect the industry-concentration index in the definition of PRDFF. However, it does not make any significant difference in the empirical results. It should be noted that in the construction of ASY, one of required conditions is the unbiasedness of ASY, which is satisfied by reflecting the concentration index.

The use of the deviation squared does not make any critical difference in the estimation results.

This study classifies 15 OECD countries into 5 regional groups: (1) Austria, Belgium, Netherlands, (2) Italy, Spain, (3) Australia, Canada, United Kingdom, United States, (4) Denmark, Finland, Norway, Sweden, and (5) Japan, Korea.

In our single equation estimation, three different covariance matrices of error terms were considered: homoskedastic (equivalent to IV approach), heteroskedastic, and within-country homoskedastic (but heteroskedastic across countries) covariance. However, this consideration does not contribute to significant differences in either the magnitude or the statistical significance of the estimates, so we report the standard errors based on the homoskedasticity assumption for brevity

This result is derived from the following calculation: (.11*.121)/.018=.739.

This result is derived from the following calculation: (.03+1.35*.03)*.288/.018=1.128

Since we expect the partial effect of terms of trade shock to be zero in a closed economy, the intercept of −0.69 in this equation may be puzzling. It is important to remember that this relationship can be the 1^st order approximation of a nonlinear equation.

Our estimate 0.16 means that per capita government expenditure rises by (1+0.16/GOV) percent with a 1percent increase in per capita income, suggesting the elasticity of 1.45.

We can examine the effect of population density on government size, by imposing the restriction that the absolute values of the coefficients on POP and LAND are identical. All the estimation results of ^{equations (7)} and ⁽⁸⁾ hardly change by imposing this restriction. The coefficient on population density is .043 and it is highly significant.

A formal test for the relevance of IV approach, which is often called “Hausman Test,” is also performed. The test results confirm that the difference between OLS and IV estimates is statistically significant in all cases. The test statistics are available upon request.

As we can see from the high significance and the large differences between instrumented and uninstrumented estimates, the estimation results do not seem to suffer from the presence of weak instrument. In the case of ^{equation (8)}, the F-statistic for first stage regressions is well above the threshold of 10 suggested by Staiger and Stock (1997), which is relevant when only one endogenous variable is included as a regressor.

Government size has a ‘negative’ influence on intersectoral fluctuation while the latter has a ‘positive’ effect on the former

The average EXP is 35.1 percent, which is the sum of NSTEXP (13.6 percent) and STEXP (21.5 percent).

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Government Size and Intersectoral Income Fluctuation: An International Panel Analysis

Author: Mr. Daehaeng Kim and Chul-In Lee

Volume/Issue:: Volume 2007: Issue 093

Publisher:: International Monetary Fund

ISBN:: 9781451866575

ISSN:: 1018-5941

Pages:: 34

DOI:: https://doi.org/10.5089/9781451866575.001

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IIF and Variance of GDP growth rate: 1981-1998

Table 7.

Uncertainty Effect on Government Size: Equation (8)

Dependent Variable	Estimation Method ^1/	ASY^2/		ASY^3/
Dependent Variable	Estimation Method ^1/	INC included		INC excluded
EXP	OLS	0.504	(0.208)	0.358	(0.208)
	IV₁	5.287	(2.184)	3.671	(1.488)
	IV₂	4.023	(1.525)	3.102	(1.226)
NSTEXP	OLS	0.005	(0.091)	-0.089	(0.093)
	IV₁	1.865	(0.882)	1.034	(0.587)
	IV₂	0.832	(0.517)	0.399	(0.438)
STEXP	OLS	0.499	(0.174)	0.448	(0.171)
	IV₁	3.422	(1.499)	2.637	(1.101)
	IV₂	3.191	(1.217)	2.703	(1.007)

^{^1/}IV₁ and IV₂ are defined as in the note 4 of Table 3.

^{^2/}INC is included as a regressor in equation (8).

^{^3/}INC is excluded from equation (8).

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Abstract

I. Introduction

II. Theoretical Framework

A. Measurement of Economic Uncertainty

B. Simple Keynesian Model

C. Openness to Trade and Intersectoral Fluctuation

III. Empirical Models and Data

A. Specification and Identification of Empirical Models

Endogeneity of openness to trade

Estimation strategy

Discussion on identifying assumptions: the preferred specification

B. Data and the Sample

IV. Estimation Results

A. Patterns of Estimates

Determinants of intersectoral income fluctuation: equation (7)

Determinants of government size: equation (8)

Accounting for differences among estimates

B. Further Results

Using other measures of government size

Checking the validity of INC as IV

V. Summary and Conculsions

APPENDIX I. PROOF OF RESULTS

APPENDIX II. THE EQUILIBRIUM OF THE OPEN ECONOMY MODEL

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