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count openness and inflation is only significant in low income countries, highly indebted countries, high inflation countries, and low inflation countries. The negative effect of capital account openness in high inflation countries is much stronger than low inflation countries.
Based on the comment by Lane and Milesi-Ferretti (2006) in which both portfolio and foreign direct investment had expanded rapidly since the 1990s and the margin has even outpaced trade openness, Badinger (2009) takes fi-nancial openness into account when doing research about inflation, and he measured financial openness in terms of the total foreign assets and liabilities as a share of GDP calculated by Lane and Milesi-Ferretti (2006). By using the cross-sectional data of 91 countries in 1985-2002, the empirical results shows that trade and financial openness both have negative and significant effects on inflation. But when doing the empirical work including trade and finan-cial openness simultaneously, the coefficients of trade and finanfinan-cial openness became negative but insignificant. Badinger (2009) restricts the model by plac-ing a statistical hypothesis that the coefficient of trade openness and financial openness are equal, and he finds that the coefficient of openness becomes neg-ative and significant. Badinger (2009) also divided the data set into OECD countries, and the empirical results show that the negative effects of openness become insignificant. According to his empirical results, Badinger (2009) sup-ports the Barro–Gordan framework argued by Romer (1993) that the optimal policy is time inconsistent when absent to a credible commitment.
2.4 The Endogeneity of Openness
Romer (1993) argues that openness may be endogenous. The import share of GDP is not only associated with country size but also depends on the country’s policy choices. A country may adopt protectionist policies and also implement other policies that benefit particular groups. It is possible that this may cause
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large budget deficits and lead to high inflation to generate seigniorage rev-enues. Romer (1993) argues that “a negative correlation between openness and inflation could arise through this channel rather than through the impact of openness on the policy makers’ incentives to pursue expansionary policies.”
To overcome the possible endogeneity of openness, Romer (1993) does the em-pirical work by using the land area as an instrumental variable. Land area is negatively related with openness,and it could be assumed to be uncorrelated with the policy. After adding the land area as an instrumental variable to the empirical work, the instrumental variable estimates are negative and sig-nificant. Furthermore, the empirical results show that the effect of openness becomes stronger after dealing with the potential endogeneity of openness.
In addition to the land area, population is an alternative measurement of country size. When both land area and population are used as instrumental variables,the openness has a negative and significant effect on inflation. But the negative effect becomes weaker and insignificant when Romer (1993) uses population as an instrumental variable, and he leaves these findings as a puzzle.
Gruben and Mcleod (2002) argue that countries with low inflation are prob-ably able to ease capital controls. Thus, when the empirical work between the capital account openness and inflation, they use country size (total 1980 GDP and land area) as an instrument variable to solve endogeneity. The empirical results show that the coefficient of capital account openness is negative and significant by using the two stage least square (2SLS) method, and the effects of the capital account openness increases.
Bowdler and Malik (2006) argue that inflation volatility may bring uncer-tainty and cause the trade to fall. And thus the causation of openness and inflation volatility becomes the reverse direction and the effect of openness on inflation volatility will be overstated. According to Frankel and Romer (1999), the lagged population size is a time-varying element of a standard gravity
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model of trade flows. They address the potential endogeneity of openness by using a lagged value of openness and a lagged value of population as instru-ment variables. After completing the empirical work by the GMM methods of Arellano and Bond (1991) and Arellano and Bover (1995), Bowdler and Malik (2006) find that the lagged population size can help to predict the effect of openness and their empirical results show that openness has a significant effect to reduce inflation volatility.
From the opinions of Gupta (2008), there are two reasons why capital controls may be endogenous. First, it is possible that countries are expected to remove their capital controls when inflation is under control. Because inflation may influence the policy choices, the coefficient of capital account openness may be biased. Second, capital controls are correlated with other determinants of inflation. Gupta (2008) makes use of the lagged values of capital account openness as an instrument variable. After using the GMM method of Arellano and Bond (1991) to view the empirical work, his empirical results show that the effects between capital account openness and inflation are negative and significant.
Badinger (2009) quotes the argument of Romer (1993) that countries may adopt protectionist policies and also implement other policies favoring par-ticular interest groups. It is possible that these policies could lead to large budget deficits and high rates of inflation to generate seigniorage revenues, so that trade openness and financial openness may be endogenous. He uses the geographical characteristics which are suggested by Frankel and Romer (1999) to identify the effect of openness. After adding the geographical characteristics as an instrument variable, Badinger (2009) finds that openness and financial openness have a negative effect on inflation.
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3 Model
3.1 Quantile Regression
In most of the research studies, the researchers usually apply the OLS method and the least absolute deviation method to their empirical work. The OLS method generates the estimators by minimizing the sum square of error. It is convenient to use the OLS method to get the estimator, but there exists some shortcomings of this method. The OLS estimators cannot fully describe the different conditional quantile functions, and it can just reveal the average effect that independent variables are influenced the dependent variables. Ad-ditionally, it may be influenced by the outliers for the OLS method. Therefore, Koenker and Bassett (1978) propose the QR to make up the shortcomings of the OLS method.
Let yiand xi be two random variables, and suppose that the θth conditional quantile of yi is defined as Qyi(θ|xi). The θth regression quantile, 0 < θ < 1, is defined as
yi = x0iβ(θ) + ei(θ), or
Qyi(θ|xi) = x0iβ(θ),
where yi is the 1×1 independent variable, xiis the k×1 vector of the dependent variable, β(θ) is the k × 1 parameters of interest to be estimated, ei(θ) is the 1 × 1 error term, and x0iβ(θ) is the θth conditional quantile of yi. The ˆβ(θ) is defined as the solution to the minimization problem of the θth regression
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where ρθ(·) is the check function in which
ρθ(α) =
As shown in equation (1), the QR method generates the estimators by minimiz-ing the weighted sum of the least absolute error when given the θth quantile.
Powell (2002) uses the generalized method of moments (GMM) to generate the large sample properties of QR. The large sample properties of QR can be shown as:
and fe(θ)|x is the probability distribution function of error term under x.