開放性、犧牲比率與通貨膨脹：工具變數分量迴歸模型之應用 - 政大學術集成

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(1)國立政治大學經濟學系碩士論文指導教授: 林馨怡博士. 政治大. ‧. ‧ 國. 學. Openness,立Sacrifice Ratio, and Inflation: Application of Instrumental Variable Quantile Regression. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. 研究生: 侯俊宇中華民國九十九年七月. v.

(2) 謝詞經過了一年的努力, 碩士論文終於完成。轉眼間, 在政大也待了六年。在碩士論文的寫作期間, 感謝林馨怡老師在論文完成過程中給予我諸多的鼓勵與指引, 讓我學習到許多東西並且完成論文。也謝謝口委老師陳旭昇教授及林常青教授對於論文的寶貴意見, 使的論文可以更加充實完善。此外, 感謝大學財政系的伙伴們, 我們一起考上的研究所又各自的. 政治大. 努力朝自己的目標邁進, 謝謝你們這段時間的陪伴, 陪著我打球、耍. 立. 宅、遊山玩水抒解壓力。 Go! Fight! Win! 謝謝經濟研究所的同學們. ‧ 國. 學. 和我一起度過許多難關, 尤其是浩榜兄, 我們一起聯手解決了諸多難. ‧. 題。謝謝親愛的爺爺奶奶, 讓我每次回南部都有雞腿可以吃。. sit. y. Nat. 最後, 謹將本篇論文獻給我最愛的父母親, 謝謝他們在我背後默默. io. n. al. er. 的支持我完成學業。. Ch. engchi. i Un. v. 侯俊宇 2010 年 7 月. 於國立政治大學經濟研究所.

(3) Abstract The relationship between openness and inflation is an important issue in macroeconomics. Romer (1993) uses the models of Kydland and Prescott (1977) and Barro and Gordan (1983) to argue that greater openness will reduce the policymakers’ incentive to deviate from the rule. Cukierman, Webb, and Neyapti (1992) and Romer (1993) have an idea that countries with less political stability have a higher probability to violate the pre-committed monetary policies. In addition, as proposed by Romer (1993), the openness may be endogenous when analyzing the relationship between openness and infla-. 政治大 proposed by Galvao (2008), 立 Galvao and Montes-Rojas (2009), and Harding tion. Thus, we apply instrumental variable quantile regression for panel data. ‧ 國. 學. and Lamarche (2009) to test whether or not the negative effects of openness is stronger when inflation is higher. We also do the empirical work between openness and the sacrifice ratio to test the mechanism that openness affects. ‧. inflation established by Romer (1993). After dealing with the potential en-. sit. y. Nat. dogeneity of openness, we find that when the inflation is higher the negative effect of openness is stronger. As the argument of Romer (1993), our empirical. io. n. al. er. results show that the time inconsistency problem is more serious in countries. i Un. v. with higher inflation. But our empirical results show that the effect of open-. Ch. engchi. ness on the sacrifice ratio is positive which is different from the mechanism established by Romer (1993). Key Word: Openness, Inflation, Sacrifiece Ratio, Quantile Regression, Endogeneity, Panel Data. 3.

(4) Contents 1 Introduction. 1. 2 Literature Review 2.1 The Openness and Inflation . . . . . . 2.2 The Openness and Sacrifice Ratio . . . 2.3 The Financial Openness and Inflation 2.4 The Endogeneity of Openness . . . . .. . . . .. 4 4 9 13 14. 3 Model 3.1 Quantile Regression . . . . . . . . . . . . . . . . . . 3.2 Quantile Regression with Endogeneity . . . . . . . . 3.3 Quantile Regression for Panel Data with Endogeneity 3.3.1 Estimation . . . . . . . . . . . . . . . . . . . . 3.3.2 Large Sample Properties . . . . . . . . . . . .. 17 17 18 21 21 24. 立. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 政治大. ‧. ‧ 國. 學. . . . . . . . . .. . . . . . . . . .. n. er. io. sit. y. Nat. 4 Empirical Results 4.1 Data . . . . . . . . . . . . . . . . . . . . 4.2 Cross-Sectional Analysis . . . . . . . . . 4.2.1 The Openness and Inflation . . . . al v 4.2.2 The Openness ni C h and SacrificeURatio 4.3 Panel Data Analysis e.n. g. c. h. i. . . . . . 4.3.1 Basic Results . . . . . . . . . . . . 4.3.2 Exchange Rate Regime . . . . . . 4.3.3 The Degree of Indebtedness . . . . 4.3.4 The Degree of Income . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. 28 28 31 31 33 35 35 38 40 42. 5 Conclusion. 43. Reference. 45 I.

(5) A Tables and Figures. 50. B Data Description. 72. C List of Countries C.1 All Countries . . . . . . . . . C.2 Severely Debted Countries . . C.3 Moderately Debted Countries C.4 Less Debted Countries . . . . C.5 High Income Countries . . . . C.6 Middle Income Countries . . C.7 Low Income Countries . . . .. 73 73 73 74 74 74 74 75. 立. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. 政治大. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. II. i Un. v. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . ..

(6) List of Tables 1 2 3 4 5 6 7 8 9 10 11. Cross-Sectional Descriptive Statistics . . . . . . . . . 50 Main Descriptive Statistics . . . . . . . . . . . . . . 51 Descriptive Statistics with Exchange Rate Regime . . 52 Descriptive Statistics for Different Degree of Debted . 53 Descriptive Statistics for Different Degree of Income . 54 Cross-Section Analysis: Openness and Inflation . . . 57 Cross-Section Analysis: Openness and Sacrifice Ratio 59 Openness and Inflation: Basic Results . . . . . . . . 61 Openness and Inflation: Another Measure of Openness 63 Openness and Inflation: Exchange Rate Regime . . . 65 Openness and Inflation: Different Degree of Indebtedness . . . . . . . . . . . . . . . . . . . . . . . . . . 67 12 Openness and Inflation: Different Degree of Income . 69. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. III. i Un. v.

(7) List of Figures 1 2 3 4 5 6 7 8. Inflation in 1973-2008 . . . . . . . . . . . . . . . . . 55 Histogram . . . . . . . . . . . . . . . . . . . . . . . . 56 Cross-Sectional Analysis: Openness and Inflation . . 58 Cross-Sectional Analysis: Openness and Sacrifice Ratio 60 Openness and Inflation: Basic Result . . . . . . . . . 62 Openness and Inflation: Another Measure of Openness 64 Openness and Inflation: Exchange Rate Regime . . . 66 Openness and Inflation: Different Degree of Indebtedness . . . . . . . . . . . . . . . . . . . . . . . . . . 68 9 Openness and Inflation: Different Degree of Income . 70 10 Openness and Inflation: Comparioson . . . . . . . . 71. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. IV. i Un. v.

(8) 1 Introduction Most central banks in the world are seeking to stabilize output growth and reduce inflation. When talking about the subject of inflation, we can trace this back to the topic of Phillips curve. Sacrifice ratio is used to measure the output-inflation tradeoff of Phillips curve. How to stabilize output growth without drifting the inflation is a subject of inflation and sacrifice ratio that has been discussed for many years. Kydland and Prescott (1977) and Barro and Gordan (1983) argue that policymakers have an incentive to deviate from the rule because of the “time inconsistency problem.” But when people ratio-. 政治大 rates of inflation are excessive. Romer (1993) uses the model of Kydland and 立 Prescott (1977) and Barro and Gordan (1983) to discuss the negative relationnally expect the policymaker’s objectives, these surprises cannot occur and the. ‧ 國. 學. ship between openness and inflation. He argues that the increase of openness will cause the output-inflation tradeoff to fall, and therefore the central bank. ‧. has a smaller incentive to generate surprise inflation in the more open eco-. y. Nat. nomics because the Phillips curve is steeper. Furthermore, Romer (1993) not. sit. only uses theory to explain this phenomenon, but also uses his empirical results. er. io. to support the negative relationship between openness and inflation.. al. n. iv n C ness and inflation, openness mayhbe endogenous. U e n g c h i A country may adopt protecRomer (1993) argues that when analyzing the relationship between open-. tionist policies and also adopt other policies that are beneficial to particular. groups. It is possible that this may cause large budget deficits and lead to high inflation to generate seignorage revenues. Gruben and Mcleod (2002) and Gupta (2008) argue that countries with low inflation are probably able to ease capital controls, and capital controls may be correlated with other determinants of inflation. Therefore, if we ignore the endogeneity of openness we won’t be able to understand the real effects of openness on inflation. So we use instrument variables such as a lagged term of openness, population, and 1.

(9) gravity estimates to solve the potential endogeneity of openness. Cukierman, Webb, and Neyapti (1992) and Romer (1993) have an idea that countries with less political stability have a probability to violate the precommitment monetary policy. Therefore, these countries have a more serious time consistency problem. As a result, we have applied the quantile regression (QR) model generated by Koenker and Bassett (1978) to this topic. QR method can help us understand whether or not the negative relationship between openness and inflation would change at different quantile. We apply the instrumental variable quantile regression for panel data generated by Galvao (2008), Galvao and Montes-Rojas (2009), and Harding and Lamarche (2009). 政治大 After dealing with the potential endogeneity of openness, our 立. to explore the relationship between openness and inflation for 127 countries in 1973-2008.. empirical results show that the negative effect of openness on inflation be-. ‧ 國. 學. comes stronger when the inflation is higher. This supports the argument that countries with higher inflation have a more serious time consistency problem.. ‧. Moreover, when we add the exchange rate regimeto the empirical work, we find. y. Nat. that the relationship between openness and inflation is significantly negative.. io. sit. We also divide the samples into different groups according to the countries’. er. degree of indebtedness and income to discover that the time inconsistency. al. n. iv n C h etry In addition, many researchers h i theU mechanism established by n gtoctest. problem is more severe in severely indebted and low income countries.. Romer (1993) that openness causes inflation to fall by reducing the sacrifice ratio. But the empirical results such as Ball (1994) and Temple (2002) indicate doubts on the mechanism established by Romer (1993). As we apply the QR method to the relationship between openness and the sacrifice ratio we found that the positive effect of openness is stronger when the sacrifice ratio is higher - this differs from Romer’s (1993) argument. Danels, Nourzad, and VanHoose (2005) argue that the Barro-Gordan framework stresses too much on the in-. 2.

(10) teraction between openness and the output-inflation tradeoff. Furthermore, our empirical results support the model of Danels and VanHoose (2006) which state that even though greater trade openness increases the sacrifice ratio, it also has a negative effect on inflation. The remainder of this paper is organized as follows: section 2 provides the literature review, section 3 defines the empirical model, section 4 presents the empirical results, and section 5 describes our conclusions.. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 3. i Un. v.

(11) 2 Literature Review 2.1 The Openness and Inflation The relationship between inflation and openness is an important issue in macroeconomics. Romer (1993) uses the Kydland and Prescott (1977) and Barro and Gordan (1983) model to explain the negative relationship between trade openness and inflation. He argues that greater openness will reduce the sacrifice ratio. Thus, policy makers have reduced the motive of monetary authorities to pursue expansionary monetary policy. In addition, surprise monetary expansion leads to real currency depreciation. When inflation is. 政治大. measured in terms of a consumer price index and if nominal wages are flexible. 立. or the foreign goods are used as inputs in domestic production, the effect of. ‧ 國. 學. the depreciation on the domestic price of imports will raise the domestic firms’ costs. Due to the influence of a real currency depreciation, the output gain to a. ‧. given monetary expansion will be reduced and thus the Phillips curve is likely to be steeper in relatively open economies. Based on the time inconsistency. Nat. sit. y. model by Barro and Gordan (1983), this would lead to a lower inflation rate.. io. er. Romer (1993) uses cross-sectional data from 114 countries in 1973-1988 to deal with his empirical work. He finds that a higher trade openness was. n. al. Ch. i Un. v. associated with lower inflation. When central bank independence and political. engchi. instability are added to the empirical model, the negative openness-inflation relationship is much stronger in countries that are less stable and have a less independent central bank. Romer (1993) also uses a variety of subsamples to work with this empirical work. For example, when he eliminates the countries in which their mean inflation is greater than 30 percent, the negative effect of inflation on trade openness becomes weak. Moreover, when he classifies the full sample according to different regions and OECD countries, there is no evidence that the coefficient of trade openness is significant. Furthermore,. 4.

(12) Romer (1993) shrinks the sample to eighteen highly developed countries, and he finds that the coefficient of trade openness is insignificant. Lane (1997) provides further research to relate trade openness and time consistent inflation. Romer (1993) argues that the more open countries tend to gain less from surprise monetary expansion. This explanation applies only to countries which are large enough to affect the structure of international relative prices. Lane (1997) establishes a general equilibrium model along with the time inconsistency model of Kydland and Prescott (1977) and Barro and Gordan (1983) to show that the inverse relationship of openness and inflation holds even for economies which are too small to affect the structure of international. 政治大 on his empirical work, and the empirical results support the argument that 立. relative prices. Moreover, he uses the same sample of Romer (1993) to build. the relationship between trade openness and inflation is negative. After the. ‧ 國. 學. country size is held constant, Lane (1997) finds that the effect of trade openness is even stronger in OECD countries and in eighteen highly developed countries. ‧. than in the full sample. The strength of the empirical results suggests that. io. y. sit. the long-run.. Nat. trade openness plays an important role in determinating the inflation rate in. er. Terra (1998) divides the sample of Romer (1993) into four groups accord-. al. n. iv n C period (1973-1981) and a debthcrisis i U e n period g c h (1982–1990).. ing to the indebtedness level, and she splits the period into a pre-debt crisis Her empirical re-. sults show that a negative relationship between trade openness and inflation only exist in the severely indebted countries during the debt crisis period. To differ from Romer (1993), Terra (1998) indicates that “the negative relationship between openness and inflation may be largely driven by the response of severely indebted countries to the debt crisis of the 1980s.” She brings up two explanations for the empirical results. One interpretation is that the severely indebted countries have a higher probability to violate the pre-commitment. 5.

(13) in monetary policy, and thus the time inconsistency problem becomes more serious. This explains why the negative effect of trade openness is only significant in severely indebted countries. Another explanation is that the absence of pre-commitment in monetary policy generates a relationship of openness and inflation, and the severely indebted countries strengthen this relationship. Additionally, Terra (1995) generates a model for further arguments. If there are two countries with the same debt situation, the less open country needs a larger exchange rate devaluation to obtain a trade surplus. Therefore, when the inflation tax is the major mechanism for resource transfer, the less open countries have higher inflation during a debt crisis.. 政治大 flation in the period of 1973-1988 with the period from 1989-1998. According 立. Bleaney (1999) contrasts the relationship between trade openness and in-. to his empirical results, the negative relationship between trade openness and. ‧ 國. 學. inflation become weak and insignificant since 1989. But Bleaney (1999) doesn’t explain why the negative relationship between trade openness and inflation is. ‧. no longer robust after 1989. Furthermore, Bleaney (1999) uses the exchange. y. Nat. rate regime data used by Ghosh er al. (1995) to catch on the exchange rate. io. sit. regime effect, and the positive coefficient of the exchange rate regime implies. er. that a shift towards flexibility is associated with a higher inflation rate. Af-. al. n. iv n C U insignificant in 1989-1998. h einn1973-1988 openness are significantly negative g c h i but. ter considering the role of the exchange rate regime, the coefficients of trade. Since the exchange rate regime is such a significant variable, Bleaney (1999) argues that it needs to be considered more deeply. He concludes that because of the globalization of the international capital market, the pegged exchange rate regime is faced with more speculative challenges than ever before. In contrast to the period of 1973-1988, developing countries need to find a way to combine flexible exchange rates with low inflation. Gruben and McLeod (2004) apply the generalized method of moments. 6.

(14) (GMM) dynamic panel methods issued by Arellano and Bover (1995) to their empirical work, and they use the five-year average data for 1971-2000 which cover the periods from 1973-1989 for Romer (1993) and Terra (1998). Following Terra (1998), they separate the countries according to their degree of indebtedness and separately split the period into the 1980s debt crisis and other periods. Consistent with Terra (1998), their pooled ordinary least square (OLS) estimates reveal that a negative relationship between trade openness and inflation of severely indebted countries only exist during a debt crisis, but no severely indebted country is significant over all periods. But different from Bleaney (1999), the empirical results of Gruben and McLeod (2004) show that. 政治大 the 1990s which is a bit surprising. They cite the interpretation of Romer 立. the negative relationships of openness and inflation have strengthened during. (1993) to explain why openness might reduce inflation.. ‧ 國. 學. Although the long-run effect of trade openness can be examined by using cross-sectional data, Alfaro (2005) tests whether a negative relationship be-. ‧. tween trade openness and inflation exists in the short-run. She takes a panel. y. Nat. data set from 1973 to 1998 into account. After controlling for the country. io. sit. fixed effect and time fixed effect, her empirical results show that the coeffi-. er. cient of trade openness is positive which is inconsistent with Romer (1993).. al. n. iv n C h e nepisodes tion greater than 50%), low inflation i U inflation less than 2%), g c h (average Furthermore, Alfaro (2005) controls for high inflation episodes (average infla-. and a high openness sample (imports as a percentage of GDP greater than 100%) and finds that the effects of trade openness on inflation are significantly positive. According to her empirical results, she argues that greater openness does not reduce the motive of monetary authorities for inflation. Thus, Alfaro (2005) began to ask what other mechanisms might limit the benefits of unanticipated monetary expansions in the short-run. Based on Calvo and. Vegh (1999), the economies with more open systems will have a more effi-. 7.

(15) cient mechanism for pegging the exchange and reducing inflation. In addition, Frankel (1999) emphasized that the fixed exchange rate can reduce the transaction costs and the exchange rate risks can discourage trade. Therefore, Alfaro (2005) brought an exchange rate regime into the empirical work, and the coefficient of openness is also positive and significant. More importantly, she found that the exchange rate regime has a negative effect on inflation when using the exchange rate regime which was defined by the International Monetary Fund (IMF) and Reinhart and Rogoff (2003). The empirical results show that when the exchange rate regime moves from floating to fixed, the inflation will fall. According to the empirical results, Alfaro (2005) believes that the fixed. 政治大. exchange rate regime plays a more important role than openness to influence. 立. inflation in the short-run.. Recently, Nasser, Sachsida, and Mendonca (2009) try to verify that more. ‧ 國. 學. open economies can reduce inflation. They explore the relationship between trade openness and inflation in 152 countries during the period of 1950-1992. ‧. and find that the principles of Romer (1993) hold when using panel data.. y. Nat. Moreover, they also restrict the data set to the full period (1973-90), the pre-. io. sit. debt crisis period (1973-81), and the debt crisis period (1982-90) and split. er. the whole data set into four groups: severely indebted countries, moderately. al. n. iv n C hypothesis of Terra (1998) that h the is due to the severely i U enegative n g c hrelationship. indebted countries, less indebted countries and other countries to test the. indebted countries during the debt crisis period. However, different from the findings of Terra (1998), the negative relationship between trade openness and inflation is realized not only in severely indebted countries but also in other countries during the full period. These findings support the model of Barro and Gorden (1983) who argued by Romer (1993): more open economies should have lower inflation rates. An absence of a pre-commitment in monetary policy will lead to inefficiently high inflation.. 8.

(16) Lin and Chen (2010) use the panel data in 1973-2007 to explore the relationship between openness and inflation. They argue that the characteristic of inflation is right-skewed and it will be influenced by outliers, so they apply QR for panel data of Koenker (2004) to their empirical work. After they do the empirical work between openness and inflation with QR, they find that when the quantile is higher the negative effect of openness on inflation becomes stronger. Furthermore, when they add the exchange rate regime to the empirical work between openness and inflation, they find that the negative relationship between openness and inflation is not affected by exchange rate regime.. 2.2. 政治大 The Openness and Sacrifice Ratio 立. ‧ 國. 學. Despite the relationship that exists between openness and inflation, an important theoretical mechanism that affects these two topics was established by Romer (1993) and is the relationship between openness and the output-. ‧. inflation tradeoff. Romer (1993) argues that greater openness will cause the. sit. y. Nat. output-inflation tradeoff to fall and reduce the incentive for monetary authorities to inflate. It implies that the output-inflation tradeoff should be negatively. io. n. al. er. related to openness. Ball (1994) selected disinflation periods as his sample pe-. i Un. v. riod to build the data set and calculated the sacrifice ratio (or output-inflation. Ch. engchi. tradeoff) for 19 OECD countries. Because the annual output data are available in only some of the countries, Ball (1994) calculated both the quarterly data and the annual data. The denominator of the sacrifice ratio is the change in trend inflation and the numerator is the sum of the output losses. Where the change in trend inflation refers to the differences between inflation at the peaks and troughs, and the sum of the output losses stand for the deviations between actual output and its full employment or trend level. When calculating the trend inflation in quarter t, Ball (1994) uses the average of inflation. 9.

(17) from t − 4 through t + 4. By using the quarterly and annual data, his basic empirical result shows that the coefficient of openness on the sacrifice ratio is positive in quarterly data and negative in annual data, but they are not significant. These empirical results cause Ball (1994) to doubt the argument of Romer (1993) that openness reduces inflation by changing the output-inflation tradeoff. Temple (2002) uses a variety of measures of the output-inflation tradeoff to test the relationship between openness and the output-inflation tradeoff. When he considers the data set calculated by Ball (1994) to examine the relationship between trade openness and output-inflation tradeoff, his empirical. 政治大 further check on this empirical work, Temple (2002) also used data calculated 立 results show that the coefficient of openness is negative but insignificant. For a. by Jordan (1997), and he considered the same time periods as Ball (1994).. ‧ 國. 學. Jordan (1997) calculated the “benefit ratio” by using the gain in output as a numerator and increasing inflation as a denominator. After applying the data. ‧. of Jordan (1997) to the empirical work, the effect of openness on the bene-. y. Nat. fit ratio is negative and insignificant. Even more, Ball, Mankiw, and Romer. io. sit. (1988) have estimated the output-inflation tradeoff for a large number of devel-. er. oping and developed countries to make a study of New Keynesian Economics.. al. n. iv n C h eshow account, and the empirical results coefficient of openness is posi U n gthat c hthe. Temple (2002) takes the data set of Ball, Mankiw, and Romer (1988) into. itive and insignificant. By using these three kinds of output-inflation tradeoff. data, Temple (2002) doesnot find a robust relationship between openness and the output-inflation tradeoff. He argues that the correlation of openness and inflation is something of a puzzle, and he argues that it became a little harder to explain the negative relationship between trade openness and inflation in terms of time consistency models. Danels, Nourzad, and VanHoose (2005) use the output-inflation tradeoff. 10.

(18) calculated by Ball (1994) and the regression models formed by Temple (2002) in their research, and they take the degree of central bank independence and the interaction term involving central bank independence and trade openness into account. Their empirical work shows two different aspects from Temple (2002): First is that trade openness has a positive and significant effect on the output-inflation tradeoff. Second, the R-square value is much higher than the values obtained by Temple (2002). Danels, Nourzad, and VanHoose (2005) also find that the coefficient of central bank independence is positive and significant. Their empirical results show that a more independent central bank should be associated with a larger sacrifice ratio. Additionally, the coefficient. 政治大 negative and significant, and it reflects that trade openness will reduce the 立. of interaction term between central bank independence and trade openness is. effect of central bank independence on sacrifice. According to the empirical. ‧ 國. 學. results of Danels, Nourzad, and VanHoose (2005), they emphasize the role of central bank independence when dealing with empirical work about the sacri-. ‧. fice ratio. They argue that the Barro-Gordan framework stresses too much on. y. Nat. the interaction between openness and the output-inflation tradeoff, and they. io. sit. quote the theoretical interpretations of Danels and VanHoose (2006) and Razie. er. and Yuen (2002) to emphasize “the importance of an imperfectly competitive. al. n. iv n C U bank independence”. h eopenness reduction generated by increased and i central ngch. goods markets and the degree of nominal wage rigidity rising due to inflation. Danels and VanHoose (2009) develope a theoretical model of an open eco-. nomic that trades openness and capital mobility as having a positive effect on the sacrifice ratio, and they use the data from Ball (1994) to deal with their empirical work. Consistent with their theoretical model, their empirical results show that the trade openness and capital mobility have positive and significant effects on the output-inflation tradeoff respectively. They also find that greater wage duration enhances the positive effect of capital mobility on the. 11.

(19) sacrifice ratio. Overall, their empirical results of cross-sectional data are consistent with the theoretical model that the two forms of globalization include trade openness and capital mobility and they tend to have positive effects on the sacrifice ratio. In addition to exploring the relationship between openness and inflation, Badinger (2009) tries to test the theoretical mechanism inference of Romer (1993) that openness affects inflation. He uses the same data set as the empirical work between openness and inflation to discuss the effect of openness on output-inflation tradeoff and to identify the channel that openness affects inflation. To obtain the data of the output–inflation tradeoff, Badinger (2009). 政治大 defines openness as trade openness and financial openness, and his empirical 立 follows Lucas (1973) to estimate the average output-inflation tradeoff. He. results show that the coefficient of trade openness is positive and insignificant. ‧ 國. 學. and the coefficient of financial openness is positive and significant. But after he placed a statistical hypothesis that the coefficient of trade openness and fi-. ‧. nancial openness are the same, the coefficient became positive and significant.. y. Nat. The empirical results between openness and the output-inflation tradeoff is in-. io. sit. consistent with the Barro-Goden framework which was interpreted by Romer. er. (1993), but it had a uniform result with the theoretical model of Danels and. al. n. iv n C hen (2007) developed a new Keynesian open economic g c h i U model which showed that. VanHoose (2006, 2009) and Razin and Loungani (2007). Razin and Loungani. globalization induces the policy maker to place more emphasis on reducing inflation than on narrowing the output gap in their model, and, therefore, both openness and capital flows have a positive effect on the output-inflation tradeoff.. 12.

(20) 2.3 The Financial Openness and Inflation Gruben and Mcleod (2002) find that two-thirds of the countries in Romer’s (1993) data set have eased the capital account or current account restrictions in the 1990s, so they presented empirical work to link the capital account openness to lower inflation. They added a capital account openness index developed by Quinn and Toyoda (1996) to their empirical work, and they constructed a capital control index established from three current account and capital account restrictions tracked in the IMF’s Annual Report on Exchange-rate Arrangements and Exchange Restriction. The empirical results show that both. 政治大. of the two indices have negative and significant effects on inflation. Gruben and Mcleod (2002) also focus on the disinflation periods of 1990s, and their. 立. empirical results in 1990s show that capital account openness has a negative. ‧ 國. 學. and significant effect on inflation.. Other measures of financial openness are the liberalization of capital ac-. ‧. counts. Gupta (2008) build a theoretical model to show that capital accounts will lower inflation, and he uses the panel data set in 1980-2003 for 163 coun-. Nat. sit. y. tries to deal with the empirical work. He introduces the Chinn-Ito index which. al. er. io. was developed by Chinn and Ito (2006) to measure the capital account liber-. n. alization. Based on the IMF’s Annual Report on Exchange-rate Arrangements. Ch. i Un. v. and Exchange Restriction, Chinn and Ito (2006) used four binary variables of. engchi. the capital and current account transactions which require the surrendering of export proceeds and the presence of multiple exchange rates to construct the Chinn-Ito index. After controlling for GDP per capita, budget deficits, exchange rate regimes, political stability, central bank independence and trade openness, his empirical results showed that capital account openness has a negative and significant effect on inflation. In addition, he also divides the sample into different samples by the degree of inflation, income and indebtedness. The empirical results show that a negative relationship between capital ac13.

(21) 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 financial 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. 政治大 that trade and financial openness both have negative and significant effects 立. cross-sectional data of 91 countries in 1985-2002, the empirical results shows. on inflation. But when doing the empirical work including trade and finan-. ‧ 國. 學. cial openness simultaneously, the coefficients of trade and financial openness became negative but insignificant. Badinger (2009) restricts the model by plac-. ‧. ing a statistical hypothesis that the coefficient of trade openness and financial. y. Nat. openness are equal, and he finds that the coefficient of openness becomes neg-. io. sit. ative and significant. Badinger (2009) also divided the data set into OECD. er. countries, and the empirical results show that the negative effects of openness. al. n. iv n C hen ports the Barro–Gordan framework argued byi Romer g c h U (1993) that the optimal become insignificant. According to his empirical results, Badinger (2009) sup-. 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. 14.

(22) large budget deficits and lead to high inflation to generate seigniorage revenues. 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 empirical 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 significant. Furthermore, the empirical results show that the effect of openness. 政治大 In addition to the land area, population is an alternative measurement of 立. becomes stronger after dealing with the potential endogeneity of openness.. country size. When both land area and population are used as instrumental. ‧ 國. 學. 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.. y. Nat. Gruben and Mcleod (2002) argue that countries with low inflation are prob-. io. sit. ably able to ease capital controls. Thus, when the empirical work between the. er. capital account openness and inflation, they use country size (total 1980 GDP. al. n. iv n C h ofe ncapital results show that the coefficient i U openness is negative and g c haccount. and land area) as an instrument variable to solve endogeneity. The empirical. 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 uncertainty 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. 15.

(23) 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 instrument 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. 政治大 may be biased. Second, capital controls are correlated with other determinants 立. may influence the policy choices, the coefficient of capital account openness. of inflation. Gupta (2008) makes use of the lagged values of capital account. ‧ 國. 學. 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. y. Nat. significant.. io. sit. Badinger (2009) quotes the argument of Romer (1993) that countries may. er. adopt protectionist policies and also implement other policies favoring par-. al. n. iv n C hinflation budget deficits and high rates of i U seigniorage revenues, so e n g ctohgenerate. ticular interest groups. It is possible that these policies could lead to large. 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.. 16.

(24) 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-. 政治大. ditionally, it may be influenced by the outliers for the OLS method. Therefore,. 立. Koenker and Bassett (1978) propose the QR to make up the shortcomings of. ‧ 國. 學. the OLS method.. Let yi and xi be two random variables, and suppose that the θth conditional. y. Nat. n. al. sit. io. or. yi = x0i β(θ) + ei (θ),. er. is defined as. ‧. quantile of yi is defined as Qyi (θ|xi ). The θth regression quantile, 0 < θ < 1,. CQh(θ|x ) = x β(θ), U n i y en i g ci h i. v. 0. i. where yi is the 1×1 independent variable, xi is the k×1 vector of the dependent variable, β(θ) is the k × 1 parameters of interest to be estimated, ei (θ) is the 0 ˆ 1 × 1 error term, and x β(θ) is the θth conditional quantile of yi . The β(θ) i. is defined as the solution to the minimization problem of the θth regression. 17.

(25) quantile, 0 < θ < 1: X X 1 |yi − x0i β| θ· |yi − x0i β| + (1 − θ) · n 0 0. (1). {yi <xi β}. {yi ≥xi β} n. =. 1X ρθ (yi − x0i β). n i=1. where ρθ (·) is the check function in which   θα, if α > 0, ρθ (α) =  (θ − 1)α, otherwise. As shown in equation (1), the QR method generates the estimators by minimiz-. 政治大. ing the weighted sum of the least absolute error when given the θth quantile.. 立. Powell (2002) uses the generalized method of moments (GMM) to generate. er. io. Σ(θ) := Γ(θ)−1 Ω(θ)Γ(θ)−1 ,. sit. y. ‧. √ ˆ − β(θ) → N 0, Σ(θ) , n β(θ). Nat. with. ‧ 國. shown as:. 學. the large sample properties of QR. The large sample properties of QR can be. n. a Γ(θ) l C= −E[xixife(θ)|x(0)],n i v h θ(1 e n−gθ)E(x Ω(θ) = c hiixi),U 0. 0. and fe(θ)|x is the probability distribution function of error term under x.. 3.2 Quantile Regression with Endogeneity It is possible that the variables of interest are endogenous, and the endogeneity will make the estimators inconsistent and biased. Let Y = Dα(θ) + Xβ(θ) + e , where Y is the dependent variable, D is the variable with endogenous problem, and X is the independent variable without 18.

(26) endogeneity. Assume that Y = Dα0 + Xβ0 + (Dα1 + Xβ1 )e(θ),. (2). And take the θth conditional quantile of equation (2), we can get QY (θ|D, X) = D0 α(θ) + X 0 β(θ),. (3). Equation (3) is the θth conditional quantile of Y under the θth quantile, where α(θ) = α0 + α1 Fe−1 (θ|X, D), β(θ) = β0 + β1 Fe−1 (θ|X, D), and Fe−1 (θ|X, D) stands for the θth conditional quantile of e. If we take θ as a random variable with the distribution of Uniform (0, 1), we can rewrite Y as. 政治大. Y = D0 α(U ) + X 0 β(U ).. 立. U is the unknown variable that causes the heterogeneity of Y when given. ‧ 國. 學. X and D. In other words, U stands for any factors that may influence the dependent variable, but these factors can not be observed.. ‧. Let D = δ(X, Z, V ), with δ as an unknown function, V is the unobserved. y. Nat. vector which depends on U , and Z is the instrumental vector. It is assumed. sit. that Z, X, and U are independent with each other. But D will be influenced. al. er. io. by U through the function δ because V depends on U . For this reason, there. n. iv n C Based on this model set, Chernozhukov U (2005, 2006) proposed h e n g c and h i Hansen. will be an endogenous problem with D.. the instrumental variable quantile regression (IVQR) method which mainly deals with the problem of QR for endogeneity. Define a weighted QR regression objective function as n. Qn (θ, α, β, γ) =. 1X ˆ i (θ)0 γ) · Vî (θ), ρθ (Yi − Di 0 α − Xi 0 β − Φ n i=1. (4). ˆ i (θ) ≡ Φ(θ, ˆ Xi , Zi ) is a dim(α) × 1 vector instruments, and Vî (θ) ≡ where Φ Vˆ (θ, Xi , Zi ) is a positive weight function. To simplify the model, Chernozhukov and Hansen (2006) use constant weights, Vî = 1, for the practical formulation. 19.

(27) The estimation process of the IVQR method is as below: define a grid of values {αj , j = 1, · · · , J}, and run the ordinary θth QR of Yi − Di 0 αj on Xi ˆ j , θ) and γˆ (αj , θ). and Φi (Xi , Zi ) to obtain the coefficients β(α ˆ j , θ), γˆ (αj , θ)) = arg min Qn (αj , β, γ). (β(α β,γ. Define kxkA(θ) =. √ x0 Ax, and let A(θ) be any uniformly positive definite ma-. trix. Choose α ˆ (θ) as the value among {αj , j = 1, . . . , J} that makes kγkA(θ) closest to zero: α ˆ (θ) = arg min k γˆ (αj , θ) k. 政治大. The parameters of instrumental QR is given by. 立Υ(θ) b =. b α(θ), θ) . α b(θ), β(b. ‧ 國. 學. As suggested by Chernozhukov and Hansen (2006), the instrumental variable. on Xi and Zi .. ‧. Zi can be Zi itself or the predicted value from a least square projection of Di. Nat. sit. al. er. io. v. ˆ n(Υ(θ) − Υ(θ)) → N (0, J −1 S(θ, θ0 )[J −1 ]0 ).. n. √. y. Chernozhukov and Hansen (2006) introduce that for any given probability ˆ index θ the limit distribution of Υ(θ) is. Ch. engchi. i Un. And the components of the asymptotic variance can be estimated as ˆ Ψ(θ ˆ 0 )], S(θ, θ0 ) = (min(θ, θ0 ) − θθ0 )E[Ψ(θ) Following Powell (1986), the estimator of J(θ) is Jˆ =. n 1 X ˆ i (θ)[Di0 , Xi0 ], 1(|ˆ ei (θ)| ≤ Hn )Ψ 2nHn i=1. ˆ ˆ i (θ) = [Φî (θ)0 , Xi0 ]0 , and Hn is an approwhere eî (θ) = Yi − Di0 α ˆ (θ) − Xi0 β(θ), Ψ priately chosen bandwidth. 20.

(28) 3.3 Quantile Regression for Panel Data with Endogeneity In this section, we introduce the QR for estimating panel data models using an instrumental variable. Koenker (2004) introduced a general approach to estimate the QR models for panel data, and he deals with the fixed effect with the shrinkage method. If we apply the potential endogeneity with the model of Koenker (2004), the parameters we estimated will have a bias. Galvao (2008), Galvao and Montes-Rojas (2009), and Harding and Lamarche (2009) proposed a method to solve the bias problem, and their model is similar to the model generated by Chernozhukov and Hansen (2006) on an instrumental variable for QR.. 立. 3.3.1 Estimation. 政治大. ‧ 國. 學. Consider the following QR representation of the panel data model with a measurement error. ‧. yit = zit0 η + d∗ 0it α + eit ,. Nat. y. (5). sit. where i = 1, . . . , N , t = 1, . . . , T , yit is an independent variable, zit denotes. al. er. io. the dummy variable which identifies the N distant individuals, d∗it is the p-. v. n. vector of a mismeasured dependent variable, α is the parameter of interest to. Ch. i Un. estimate, and eit is the innovation term. Suppose that we observe dit rather. engchi. than d∗it , and dit is d∗it subject to a measurement error, it , as a noisy measure, dit = d∗it + it .. (6). it is assumed to be independent and identically distributed, and the variance of it V ar(it ) = σ2 < ∞ . We can use equation (6) substituting for dit in equation (5) as yit = zit0 η + d0it α + eit − 0it α, 21. (7).

(29) The observed regressor dit will be correlated with the composite error eit − 0it α in equation (7), so there will be an endogeneity in the model. Galvao and Montes-Rojas (2009) drive an approximation to show the bias caused by endogeneity in the QR estimator by using the Angrist, Chernozhukov, and Fernandez-Val (2006) approximation. Define υ ∗ = [z 0 , d∗ 0 ]0 , Λ = [00 , 0 ]0 , υ = [z 0 , d0 ]0 = υ ∗ + Λ , and ϕ = [η 0 , α0 ]0 . And let ϕ∗ = arg min E[y − υ ∗ 0 ϕ]2 , ϕ. ϕ0 = arg min E[y − υ 0 ϕ]2 , ϕ. 政治大. where ϕ∗ and ϕ0 are the parameters which solve the minimization problem. Following the exposition of Angrist, Chernozhukov, and Fernandez-Val (2006). 立. 學. ‧ 國. and under known conditions, we can get ϕ0 =ϕ∗ − (E[υυ 0 ])−1 E[υ0 α∗ ]. (8). ‧. =ϕ∗ − (E[υ ∗ υ ∗ 0 + Λ Λ 0 ])−1 E[Λ 0 α∗ ],. y. Nat. In this case, equation (8) shows the bias caused by the endogenous problem.. sit. In addition to the panel data model exposed in equation (5), we added a. n. al. er. io. covariate xit without a measurement error to the model. Then we can rewrite the equation as below. Ch. engchi. i Un. yit = zit0 η + d∗ 0it α + x0it β + eit ,. v. (9). Note that as mentioned by Harding and Lamarche (2009), the individual effects η(θ) which enter this model are indexed by quantile θ. Because the estimated η are expected to change over the distribution of y, it is not fully standing for the effects of a “fixed effect”.. 22.

(30) We can stack the variable in equation (9) according to different i variables           0 z1t y1t d∗ 01t x01t e1t            y   z0   d∗ 0   x0   e   2t   2t   2t   2t   2t   .  =  . η +  . α +  . β +  . ,  ..   ..   ..   ..   ..            0 0 yN t zN d∗ N t x0N t eN t t Then we can stack the variable according to different t variables           y1 z10 d∗ 01 x01 e1            y   z0   d∗ 0   x0   e   2   2   2   2   2   .  =  . η +  . α +  . β +  . ,  ..   ..   ..   ..   ..            0 ∗0 0 yT zT dT xT eT. 立. 政治大. 學. ‧ 國. Finally, we can show the equation as matrices y = Zη + D∗ α + Xβ + u.. ‧. Galvao and Montes-Rojas (2009) shows that as in the least square method, it can use instrumental variable methods ωit to solve the endogenous problem,. Nat. sit. y. and the instrumental variable ωit which must affect x∗it but are indenpendent. n. al. er. io. of uit and it . Consider the θth conditional quantile function of y,. i Un. v. Qy (θ|Z, D, X) = Zη(θ) + Dα(θ) + Xβ(θ),. Ch. engchi. With variable D being endogenous in the model and the parameter of interest α being biased, Galvao and Montes-Rojas (2009) and Harding and Lamarche (2009) proposed an instrumental variable procedure to reduce the bias. Following Chernozhukov and Hansen (2006, 2008), we consider the following QR objective function . ηˆ(α, θ), α ˆ (α, θ), γˆ (α, θ) = min η,α,γ. N X T X. ρθ (yit − zit0 η − d0it α − x0it β − wit0 γ),. i=1 t=1. (10) 23.

(31) where ρθ = u(θ − I(u ≤ 0)) is the QR loss function. As suggested by Chernozhukov and Hansen (2006, 2008), the instrumental variable ωit can be ωit itself or the predicted value from a least square projection of dit on ωit and xit . The instrument variable ωit will be zero in equation (10), because the instrument variable ωit is independent of it and uit . For this reason, for a given parameter α, the QR of (yit − d0it α) on the variable (zti , xit , ωit ) should turn the coefficient of ωit into zero. Hence, we can obtain consistent estimator of η, α and β by minimizing the coefficient of ωit . The instrumental variable QR estimator for panel data can be implemented. 政治大 1) For a given quantile θ, define a grid of values {α , j = 1, . . . , J} and run 立 in two stages:. j. ‧ 國. 學. the ordinary QR of (yit − d0it α) on (zti , xit , ωit ) to get the coefficient of ηˆ(αj , θ), ˆ j , θ) and γˆ (αj , θ). β(α. ‧. ηˆ(α, θ), α ˆ (α, θ), γˆ (α, θ) := min QN T (θ, η, β, α, γ), η,β,γ. (11). sit. y. Nat. 2) To get the estimator of α ˆ (θ), choose α ˆ (θ) as the value among {αj , j =. io. al. er. 1, . . . , J} which makes kˆ γ (αj , θ)kA closest to zero. In other words, let ˆ γ (α, θ) , α ˆ (θ) = min γˆ (α, θ)0 A(θ)ˆ. (12). ˆ α(θ), θ) . ϕˆ := ηˆ(ˆ α(θ), θ), α ˆ (θ), β(ˆ. (13). n. v ni. α∈A. Ch. engchi U. ˆ where A is a positive definite matrix. After obtaining α ˆ (θ), the estimate β(θ) is given by βˆ α ˆ (θ), θ . And thus the final parameter estimators are. 3.3.2 Large Sample Properties Galvao and Montes-Rojas (2009) impose following regularity conditions:. 24.

(32) A1 The yit are indenpendent with conditional distribution functions Fit , and differentiable conditional densities, 0 < fit < ∞, with bounded derivatives fit0 for i = 1, . . . , N and t = 1, . . . , T ; A2 Let Z = IN ⊗ ιT , and ιT a T -vector of ones, D = (dit ) be a N T × dim(α) matrix, X = (xit ) be a N T × dim(β) matrix, and W = (ωit ) be a N T × dim(γ) matrix. For ˇ Π(η, α, β, θ) : = E[ θ − 1(Z 0 η + D0 α + X 0 β) X(θ)] ˇ Π(η, α, β, θ) : = E[ θ − 1(Z 0 η + D0 α + X 0 β + W 0 γ) X(θ)]. 政治大. ˇ X(θ) : = [Z 0 , X 0 , W 0 ]0 , Jacobian matrices. 立. ∂ Π(η, α, β, θ) ∂(η,α,β). and. ∂ Π(η, α, β, γ, θ) ∂(η,β,γ). are continuous. ‧ 國. 學. and have full rank, uniformly over E × A × B × L × F. The parameter space, E × A × B, is a connected set. Moreover the image of E × A × B under the map (η, β, α) → Π(η, β, α, θ) is simply connected;. ‧. io. sit. y. Nat. A3 Denote Φ(θ) = diag fit (ξit (θ)) , where ξit (θ) = zit0 η(θ)+d0it α(θ)+x0it β(θ)+ ˜ = [X, W ]0 . Then, ωit0 γ(θ), MZ = I−PZ and PZ = Z(Z 0 Φ(θ)Z)−1 Z 0 Φ(θ). Let D. n. al. er. the following matrix is invertible:. Ch. i Un. ˜ 0 MZ Φ(θ)MZ D), ˜ Jβγ = E(D. engchi. v. −1 ˜ 0 MZ Φ(θ)MZ D) and H = Now define [J¯β0 , J¯γ0 ]0 as a partition of Jβγ , Jα = E(D J¯γ0 A[α(θ)]J¯γ . Then, Jα0 HJα is also invertible;. A4 For all θ ∈ Θ = [c, 1 − c] with c ∈ (0, 1/2), α(θ), β(θ) ∈ int A × B, and A × B is compact and convex. √ √ √ A5 maxit kdit k = O( N T ); maxit kzit k = O( N T ); maxit kωit k = O( N T ).. 25.

(33) A6. Na T. → 0, for some a > 0.. Condition A1 gives the restriction on the density function of yit . As the discussion by Chernozhukov and Hansen (2006), condition A2 is for the identification of parameters. In order to guarantee the asymptotic normality, condition A3 states the invariability conditions for matrices. Condition A4 imposes compactness on the parameter space of α(θ). Such an assumption is needed since the objective function is not convex in α. Condition A5 imposes a bound on the variables. As in Koenker (2004), condition A6 allows T to grow very slowly relative to N . Under condition A1-A6 and given θ ∈ (0, 1), Galvao and Montes-Rojas. 政治大. (2009) impose that ϕ(θ) ˆ converges to a Gaussian distribution. Consider the. 立. yit = zit0 η + d0it α + x0it β + eit ,. 學. ‧ 國. following model. The objective function is ρθ (yit − zit0 η − d0it α − x0it β − ωit0 γ),. Nat. η,α,γ. ‧. min. N X T X. sit. y. i=1 t=1. al. δη δβ δα δγ ρθ (yit − ξit − zit √ − x0it √ − d0it √ − ωit0 √ ) − ρθ (yit − ξit (θ)), T NT NT NT. n. i=1 t=1. io. VN T (δN ). N X T X. er. For any αn (θ) → α(θ), we can rewrite the objective function as. Ch. engchi. i Un. v. where ξit (θ) = d0it η + x0it α + zit0 β + ωit0 γ, and in the minimum   √  δˆη (αn (θ)) T (ˆ η (αn (θ), θ) − η(θ))    √  δˆ (α (θ))   N T (αn (θ) − α(θ))    α n ˆ δn =  = √  δˆβ (αn (θ))   N T (β(α ˆ n (θ), θ) − β(θ))    √ δˆγ (αn (θ)) N T (ˆ γ (αn (θ), θ) − 0) After an appropriate transform, √ N T (ϕ(θ) ˆ − ϕ(θ)) → N (0, Ω), 26.     .  .

(34) the covariance matrix follows the asymptotic variance of. √. NT α ˆ (θ) − α(θ). and is given by ˆ(θ)−1 S ˆ(θ)J ˆ(θ)−1 , Ω=J where N. T. XX ˆ(θ) = θ(1 − θ) Ψit Ψ0it , S N T i=1 t=1 ˆ(θ) = J. N X T X 1 I(|ˆ uit (θ)| ≤ hN T )Ψit Φ0it , 2N T hN T i=1 t=1. 政治大. with Ψit = (ωit0 , x0it , zit0 )0 , Φ = (d0it , x0it , zit0 )0 , uît (θ) = yit − zit0 η − x0it β − d0it α and h is a properly chosen bandwidth.. 立. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 27. i Un. v.

(35) 4 Empirical Results 4.1 Data The data set which we used are mainly for 127 countries in 1973-2008. The data of inflation, nominal and real GDP, population, and import and export shares are taken from the World Bank’s World Development Indicators. We follow the standard approach and use the change in the GDP deflator to measure the inflation. Figure 1 shows the trend of mean inflation and quantiles. We can find that the mean inflation in 1980-1990 rises and falls quite substantially. But different from the rise and fall tendencies of mean inflation, the median inflation. 政治大. is steadier. Table 2 shows the main descriptive statistics of our data. We apply. 立. our empirical work to 127 countries covering 1973-2008, 1980-2008, and 1990-. ‧ 國. 學. 2008. In Table 2, the mean inflation in 1973-2008 is 38.44% and the median inflation is 7.62%. Moreover, the 0.75 quantile inflation is 15.21% which is. ‧. lower than the mean inflation. Figure 2 shows the histogram of inflation, the vertical axis indicates the frequency and the horizontal axis addresses the. Nat. sit. y. inflation. The data characteristics show that the trend of inflation is affected. io. by a mean effect, it cannot describe the actual case.. n. al. Ch. er. by the outliers. If we analyze the relationship between openness and inflation. i Un. v. Furthermore, we divide the whole sample into different groups according. engchi. to the countries’ degree of indebtedness and income. According to classification of the degree of income, the variation of inflation is biggest in middle income countries and smallest in high income countries, see Table 5. The data characteristics of high income countries are close to symmetric distribution. Table 4 shows the descriptive statistics of different degree of indebtedness, and it shows that the characteristics of severely indebted countries, moderately indebted countries, and less indebted countries are closed to right shaped distribution. The mean inflation in severely indebted countries is 83.05%, which. 28.

(36) is much higher than the 0.75 quantile inflation 22.92%. It stands for the variation of inflation is the most severe in highly indebted countries. If we analyze the relationship between openness and inflation by the mean effect, it may be influenced by outliers. In our empirical work, openness is defined as trade openness and financial openness. Following Romer (1993), we define trade openness as the share of imports in GDP, and we also measure it as the share of exports in GDP and the share of imports plus exports of GDP to apply to our empirical work. We quote Badinger (2009) to measure the financial openness in terms of total foreign assets plus total liabilities as a share of GDP, and the data set is. 政治大 divided by population, and we take the growth of GDP per capita as a control 立. calculated by Lane and Milesi-Ferretti (2006). GDP per capita is the GDP. variable to our empirical work.. 1. ‧ 國. 學. Following Lucas (1973), we estimate the output-inflation tradeoff with the following equation:. ‧. yt = cons + π∆xt + ρtt−1 + ϕtrend + εt ,. sit. y. Nat. where yt is the log real GDP, ∆xt is the change in the log of nominal GDP,. io. n. al. er. and the trend is a linear time trend. The π coefficient represents the output-. i Un. v. inflation tradeoff, and it shows the proportion of a shock to nominal GDP in. Ch. engchi. a particular year which is associated with an increase in real output in that year. Also, the output-inflation tradeoff can be seen as the slope of the Phillips curve. An important instrument variable we used is the gravity estimate. The data set of the gravity estimates are taken from Frankel and Rose (2002). 1. We apply the panel unit root tests of Levine, Lin, and Chu (2002) to test the unit root and find that GDP per capita does not reject the hypothesis. In other words, GDP per capita has unit roots, so we take the difference of GDP per capita to the empirical work. The t-ratio of inflation, imports, exports, population, and the growth of GDP per capita are -33.27, -18.76, -17.98, -15.95, and -35.37.. 29.

(37) Cavallo and Frankel (2008) who used the data set of Frankel and Rose (2002) to compute the gravity estimates. They measured the openness by the predicted ratio of trade to GDP based on gravity equations. The data set of Frankel and Rose (2002) consists of 41, 678 bilateral trade observations and it covers at least 98% of all trade. To get the gravity estimates, Frankel and Rose (2002), computed OLS regressions of the following form: log(Ti,j /Yi ) = cons + α log disti,j + β log popj + γcomlangi,j + δborderi,j + θareapi,j + ρlanklock + ε, where Ti,j is the bilateral trade value between countries i and j, Yi is the real. 政治大 centers of countries i and j, pop is the population of countries j, comlang 立. GDP of country i, log disti,j is the log of the distance between the economic j. i,j. is. a dummy variable that takes a value one if i and j share a common language. ‧ 國. 學. and is zero otherwise, border is a dummy variable that takes a value one if i and j share a border and is zero otherwise, areapi,j is the log of the product of. ‧. the areas (in km2 ) of countries i and j, landlock takes a value of two if i and j. y. Nat. are both landlocked, one if either i and j are landlocked, and zero otherwise.. io. sit. ε is the error term. The gravity estimates are generated by taking the fitted. er. values and summing them across bilateral partners j. But the 5-year data. al. n. iv n C hthe limited in 1973-1999 when using i U as instruments. e ngravity g c hestimates. set of Frankel and Rose (2002) are up to 1995, and thus the sample period is. Following Alfaro (2005), we take the exchange rate regime into account.. The two classifications of the exchange rate regime we used are taken from the IMF’s Annual Report on Exchange Arrangements and Exchange-Rate Restrictions and Reinhart and Rogoff (2004). The exchange rate regime of the IMF is defined as a dummy variable that takes the value of 0 if a country maintainsed a floating regime, 1 if a country maintains ed an intermediate regime, and 2 if a country a maintainsed a fixed regime. The classification of Reinhart and Rogoff (2004) is similar to the IMF, but they are based on 30.

(38) the market-determined parallel exchange rates to classify the exchange-rate regime. In their classification, they separate the exchange rate regime into five categories: 1 if a country maintainsed fixed regimes, 2 is the crawling pegs, 3 is the managed floatinging, 4 is the freely floating, and 5 is freely falling. In order to compare with the results of the IMF’s classifications, following Alfaro (2004), we define the dummy variable as 0 if the country maintained a floating regime, 3,4,5, in Reinhart and Rogoff’s (2004) classification; 1 if the country maintained a intermediate regime, 2, in Reinhart and Rogoff’s (2004) classification; and 2 if the country maintained a fixed regime, 1, in Reinhart and Rogoff’s (2004) classification.. 4.2. 治政大 Cross-Sectional Analysis 立. 4.2.1 The Openness and Inflation. ‧ 國. 學. In most of the literature studies, researchers usually use the OLS method for. ‧. their empirical work between openness and inflation. But the shortcomings of OLS estimators is that it just describes the “mean” effects of openness on. Nat. sit. y. inflation, it cannot analyze the effects of openness on inflation across quantiles.. io. show the different conditional quantile effects.. n. al. Ch. er. We apply the QR method to analyze the cross-sectional data in 1973-2008 and. i Un. v. Given θ ∈ (0, 1), and the model is defined as below:. engchi. log πi = Xi0 β(θ) + ei,θ , where πi is the inflation rate, and Xi is the independent variable including the trade openness, GDP per capita, and the constant term. Furthermore, we use the bootstrap method to estimate the stand error of QR estimators and we repeat this process 1000 times. In this section, trade openness is measured as the share of imports in GDP. Following Romer (1993) and Lane (1997), we take the log of inflation to reduce the effects influenced by the outlier inflation countries. 31.

(39) Table 6 shows the 0.1-0.9 QR estimators and the OLS estimator. In order to compare the difference between OLS and QR, we draw the OLS and QR estimators in the same figure. Figure 3 shows the cross-sectional analysis and uses estimator values as vertical axis and quantile as horizontal axis. Where the horizontal solid line is the OLS estimator, the solid curve stands for the QR estimators, and the two dotted curves represent the 95% confidence interval of QR estimators. In Table 6 and Figure 3, our empirical results show that the OLS coefficients of trade openness are negative and significant which is the same as Romer (1993). The QR estimators show that the effects of trade openness on inflation. 政治大 trade openness on inflation is stronger when the quantile is higher, and the 立. are all negative. Even more so, the QR estimators show that the effect of. QR estimators are only significant in quantile 0.3, 0.7, 0.8, and 0.9 when the. ‧ 國. 學. measure of trade openness is a share of imports in GDP. In Table 6, the OLS coefficient of trade openness is −3.22 × 10−3 , and the 0.7-0.9 quantile. ‧. coefficients are −3.19 × 10−3 , −4.34 × 10−3 , and −6.40 × 10−3 respectively.. y. Nat. The effects of trade openness on inflation at quantile 0.8-0.9 are stronger than. io. sit. the effect of OLS. The negative and significant effects of trade openness on. er. inflation only exist when inflation is high. When a country has higher inflation,. al. n. iv n C U arguments of Romer (1993). The cross-sectional empiricalhresults e n gsupport c h i the. the greater openness makes inflation drop significantly.. When there is an absence of a credible commitment, the monetary authorities have a motive to pursue expansionary monetary policy. It deserves to. be mentioned that the cross-sectional analysis describes the long run effects, and it may have no thought for the short-run characteristics. So we use the panel data to test whether or not a negative relationship exists between trade openness and inflation in the short-run. In addition, we consider the potential endogeneity of openness of the cross-. 32.

(40) sectional empirical work. Following Romer (1993), we use population as an instrument variable to deal with the potential endogeneity of trade openness and apply IVQR to the empirical work between openness and infaltion. In Table 6, our empirical results show that the IVQR estimates are all negative but only significant at the 0.7-0.8 quantiles after using the instrument to deal with the endogeneity of trade openness. It shows that the negative effect of openness is stronger when the quantile is higher when applying the QR and IVQR methods, see Figure 3. But differ from the OLS, the 2SLS estimate is negative but insignificant.. 政治大 Given θ ∈ (0, 1), and the model as below: 立 4.2.2 The Openness and Sacrifice Ratio. ‧ 國. 學. SCi = Xi0 β(θ) + εi,θ ,. where SCi is the sacrifice ratio, and Xi is the independent variable including. ‧. trade openness, mean inflation, and the variability of aggregate demand. As. y. Nat. the cross-sectional analysis between trade openness and inflation, we use pop-. io. sit. ulation as an instrument to check the empirical work and use the bootstrap. er. method to estimate the stand error of QR estimates which repeat 1000 times.. al. n. iv n C h ethenpast the output-inflation tradeoff, and h i U studies put many doubts g cliterature. Romer (1993) argues that trade openness causes inflation to fall by reducing. on the negative relationship between trade openness and output-inflation tradeoff (or sacrifice ratio). The research of Ball (1994) and Temple (2002) show that trade openness has a negative but insignificant effect on the sacrifice ratio, and their empirical results cause Ball (1994) to doubt the arguments of Romer (1993). Temple (2002) also argues that the relationship between trade openness and inflation is something of a puzzle, and he argues that it becomes a little harder to explain the negative relationship between trade openness and inflation in terms of time consistency models. Differing from Ball (1994) and 33.

(41) Temple (2002), Danels, Nourzad, and VanHoose (2005), Danels and VanHoose (2008), and Badinger (2009) have the opinion that the effect of trade openness on sacrifice ratio is positive. As mentioned above, the researchers used a different data set to apply to their empirical work, and they showed a variety of empirical results. The literature has a common point, and they all reveal the mean effect of trade openness on the sacrifice ratio. To go a step further in researching this topic, we made a breakthrough which applied the QR method to describe the different conditional quantiles. Table 7 shows that the QR estimates are all positive, which is the same as Danels, Nourzad, and VanHoose (2005), Danels and Van-. 政治大 stronger from the 0.1 quantile to the 0.6 quantile, but the positive effect of 立. Hoose (2008), and Badinger (2009). The positive effect of trade openness is. trade openness is weaker from the 0.7 quantile to the 0.9 quantile and the. ‧ 國. 學. quantile 0.9 estimate is insignificant. In addition, we used population as an instrument variable to deal with the endogeneity of openness. Figure 4 shows. ‧. that the positive IVQR estimates are higher when the quantile is higher, and. y. Nat. the 0.9 quantile estimate of IVQR is 9.18 × 10−3 which is larger than the 0.9. io. sit. quantile estimate of QR, 2.01 × 10−3 . According to the empirical results, it. er. shows that they are different from the findings from Romer (1993). We doubt. al. n. iv n C h eempirical the output-inflation tradeoff. Our i U show the positive effect of n g c hresults the mechanism in which trade openness is influenced by inflation in reducing. trade openness on the sacrifice ratio which is the same as Danels, Nourzad,. and VanHoose (2005), Danels and VanHoose (2009), and Badinger (2009), and this supports the model provided by Danels and VanHoose (2006). The model of Danels and VanHoose (2006) shows that greater trade openness reduces the pricing power of domestic firms in an economy characterized by monopolistic competition, and this lowers the output effects of unexpected price increases through a monetary expansion. As a consequence, even though greater open-. 34.

(42) ness increases the sacrifice ratio in the model of Danels and VanHoose (2006), the trade openness also has a negative effect on the inflation rate arising from discretionary monetary policy.. 4.3 Panel Data Analysis In addition to using the cross-sectional analysis to capture the long-run effect of trade openness on inflation, we also apply the panel data to analyze the relationship between openness and inflation in the short-run. Our panel data set includes 127 countries in 1973-2008, and we rely on the instrumental variable quantile regression for panel data proposed by Galvao (2008), Galvao and. 政治大. Montes-Rojas (2009) and Harding and Lamarche (2008).. 立. 學. ‧ 國. 4.3.1 Basic Results. Given the following model:. ‧. log(1 + πit ) = Zit0 η(θ) + Dit0 α(θ) + Xit0 β(θ) + eit,θ ,. y. Nat. where πit is the inflation rate, Zit denotes the dummy variable which identifies. io. sit. the N distant individuals, Dit is the trade openness with endogeneity, Xit is. er. the control variable without endogeneity including GDP per capita, and eit,θ. al. n. iv n C can not transform the inflation h byetaking log. iFollowing Gruben and McLeod ngch U is the error term. Because there exist some deflation in some countries, it. (2004), we divide the inflation rate by 100 and plus 1 to take log. In the basic empirical results, we control the growth of GDP per capita to the empirical model. As suggested by Bowdler and Malik (2006), we address the potential endogeneity of trade openness by using the lagged value of trade openness and lagged value of population as instrument variables.. Besides, Cavallo and. Frankel (2008) use the data of Frankel and Rose (2002) to compute the gravity estimates and deal with the endogeneity of trade openness by using the 35.