中国通货膨胀福利成本研究
摘要
2008年,螺旋上升的食品和石油价格推动的通货膨胀成为危及全球的最重大经济问题,抑制通货膨胀的呼声不绝于耳。那么,通货膨胀带来的福利成本损失大吗?对于同样经历通货膨胀之苦的中国,它的通货膨胀福利成本又有多大呢?对于这些问题的回答,就是本文所要研究的主要内容。
对于通货膨胀福利成本的研究始于Bailey(1956),他将通货膨胀的福利成本定义为逆货币需求函数曲线下方的面积,即名义利率从i减少到0时的消费者剩余。Lucas(2000)利用Bailey的定义计算了美国1900-1994年通货膨胀的福利成本,在双对数货币需求函数m_r=Ar~(-0.5)形式下,6%的名义利率伴随着约1.2%的国民收入福利成本,而当名义利率从12%下降到2%时,福利成本减少了GDP的1%。
随着货币理论的发展,研究者发现除了货币的价值储藏功能外,我们还要考虑货币的其他功能,例如货币的交易功能。考虑到货币的交易功能,在一个无穷期模型中分析货币对宏观经济均衡的影响(包括通货膨胀的福利成本问题)时,大多数文献常采用以下两种范式把货币整合进模型。一条途径是假定货币持有能够给消费者带来效用,从而把货币引入效用函数(Money in the utility function,MIU);另一条途径是假设消费者购买消费品必须使用货币,从而形成预付现金约束(Cash-in-advance constrain,CIA);或者是在模型中引入交易技术,假定使用货币能带来交易时间的节约,从而形成购买-时间(shopping-time)模型。
货币引入效用函数模型(MIU)考虑到个体持有货币可以带来交易便利,节省交易成本,可以有更多的休闲,有更多的时间从事生产从而获得更多的消费品,因此实际余额的持有增加了个体的效用。当通货膨胀发生时,实际货币余额就会减少,消费者的福利就会遭受损失,于是产生福利成本。Dotsey和Ireland(1996)在一般均衡的货币模型中发现,对于美国经济,年通货膨胀率4%意味着消费者0.41%的收入损失。
在预付现金(CIA)模型中,货币并不直接进入效用函数,但假定全部或部分商品的购买必须使用现金,这种约束称为Clower约束或预付现金约束。Cooley和Hansen(1989,1991)通过把预付现金约束引入真实产业周期模型,来计算预期到了的美国通货膨胀福利成本,得出10%通货膨胀的福利成本为产出的0.38%。
在Bailey(1956)的开创性研究之后,经济学家在不同的假设基础上构造了MIU模型、CIA模型,以及购买-时间模型,也得出了不同的通货膨胀福利成本。但是这些模型所蕴涵的思想却是一致的:就是通过将真实货币持有量引入效用函数或者约束条件之中,再通过模型的最优化求解到通货膨胀率与消费者效用之间的关系。通过比较不同稳态情况下的效用水平,得到通货膨胀的福利成本:在名义利率为0的情况下,消费者效用达到最大化,考虑在某个通货膨胀率水平下,需要补贴给消费者多少比例的收入或消费,才能使其效用与最优状态下的效用水平一致。所以,需要补贴给消费者的那部分收入或者消费,就是通货膨胀的福利成本。
最后,本文利用McCallum-Goodfriend模型来计算我国1992-2008年的通货膨胀福利成本。研究发现:通货膨胀的福利成本与名义利率之间存在正相关关系;1992-2008年,我国的通货膨胀福利成本并不像我们想象中的那么大,介于GDP的0.5699%—1.8732%之间;让我们深感通胀之苦的2008年,实际的通货膨胀福利成本也只是GDP的0.8031%,约合2376.5255亿元,以全国13亿人口计算,人均福利损失约为182.8096527元;即使是这17年里通货膨胀最严重的1994年(当年的通货膨胀率达到24.1%),通货膨胀的福利成本也只有GDP的1.8199%;还有一个有意义的是,亚洲金融危机后,1998、1999年我国出现了通货紧缩,两年的通货膨胀率分别为-0.8%和-1.4%,而根据我们计算的结果,两年的通货膨胀福利成本分别占GDP的1.0941%和0.7335%,这与我们通常所认为的通货紧缩是有害的相一致,也更进一步说明了只有当名义利率为零时,社会福利才达到最大化。
为进一步验证计算的结果,我们利用Bailey(1956)的方法重新计算我国的通货膨胀福利成本。我们发现:我国的通货膨胀福利成本介于GDP的0.5635%—1.8055%之间,同样很小;Bailey(1956)方法计算的结果要比我们计算的结果小,但是差异非常微小,而且随着名义利率的增长,差异也在逐渐变大。
In 2008,the inflation caused by the spiral prices of food and petroleum became the most significant economic issue all over the world.The appeal of curbing the inflation is all around.However,is the welfare cost of inflation much? To China,which is also suffered with the inflation,how much is its welfare cost of inflation? This paper will give all the answers to these questions.
The research on the welfare cost of inflation starts with Bailey(1956),he defined the welfare cost of inflation as the area under the inverse demand function---the consumers' surplus—that could be gained by reducing the interest rate from r to zero. Lucas(2000) took advantage of Bailey's definition to calculate the cost of welfare inflation of U.S.based on time series for 1900-94.For the log-log money demand function,m_r = Ar~(-0.5),at a six percent interest rate,for example,the welfare cost is one point two percent of national income.Meanwhile,when nominal interest decreases from twelve percent to two percent,then the welfare cost will reduce by one percent of GDP.
By the development of monetary theory,researchers find out that apart from the value storage function,money also have other functions,such as trading.Considering its trading function,most literature take two patterns to integrity money into the model. One pattern is that assuming holding money can bring consumers' utility,and then include money into the utility function(MIU);and another pattern is that assuming consumer must use money to buy nonstorable goods,and then it shapes the Cash-in-advance constrain,CIA,or introduce the trading techniques into the model, assuming the use of money can bring savings of trading time,then it becomes shopping-time model.
MIU model considers money holding can bring convenient,save trading cost,then have much more time to engage in production,so money holding actually increases the utility of individual.When inflation happens,it will cause the decrease of actual money balance,the loss of consumers' welfare,and then it becomes the welfare cost. Dotsey and Ireland(1996) found in a general equilibrium money model,four percent annual inflation rate cause 0.41%consumers' income loss.
In a CIA model,money can not be put into the utility function directly.So researchers assume that part of or all of the purchase of goods must use cash,and this restriction is called Clower constrain.Cooley and Hansen(1989,1991) figured out the welfare cost of inflation in USA,finding out 10%cost of inflation welfare is 0.38%of output. After Bailey(1956)'s inaugurating research,economists construct models like MIU, CIA,and shopping-time model based on different assumptions;also elicit different welfare costs of inflation.However,the same idea lies in these models,that is,by putting the actual holding money into the utility function or restrictions and optimizing the calculation of models,we can get the relationship between the inflation rate and the consumers' utility.Comparing the levels of utility under different balance conditions,we can get the welfare cost of inflation:when nominal interest rate is zero, and the consumers' utility reach its max,considering under some inflation level,what ratio of income or consume compensation is needed to leave consumers indifferent between r and 0.As a result,the part of income or consume compensation is the welfare cost of inflation.
As last,this paper uses the Mccallum-Goodfriend framework to calculate the welfare cost of inflation,based on China time series for 1992-2008.The study shows:there exist positive correlation between the welfare cost of inflation and nominal interest rate;between those years,the welfare cost of inflation is between 0.5699%of GDP and 1.8732%of GDP,not as high as what we thought before;still in the year 2008, the actual welfare cost of inflation is 0.8031%of GDP,about RMB 237.65255 billion; The individual loss of welfare is RMB 182.8096527 based on the population of 1.3 billion;even if in 1994,when the inflation is most serious reaching 24.1%,the cost of inflation welfare is only 1.8199%of GDP;and we also find another significant thing that in 1998 and 1999 when our country appeared deflation,the inflation rate of those two years is -0.8%and -1.4%respectively,after the financial crisis in Asia,those two years' welfare cost of inflation took up of 1.0941%and 0.7335%of GDP respectively, and this also states that the deflation is harmful.Moreover,this states that only when the nominal interest rate is zero,the social welfare is optimal.
To validate the results further,we use Bailey(1956)'s method recalculation the welfare cost of inflation of our country.We find:the cost of our country is between 0.5635%and 1.8055%of GDP,the same small;the results calculated by the Bailey (1956)'s method are smaller than our results,but the difference is very little,and the difference is large gradually while the increase of nominal interest rate.
对于通货膨胀福利成本的研究始于Bailey(1956),他将通货膨胀的福利成本定义为逆货币需求函数曲线下方的面积,即名义利率从i减少到0时的消费者剩余。Lucas(2000)利用Bailey的定义计算了美国1900-1994年通货膨胀的福利成本,在双对数货币需求函数m_r=Ar~(-0.5)形式下,6%的名义利率伴随着约1.2%的国民收入福利成本,而当名义利率从12%下降到2%时,福利成本减少了GDP的1%。
随着货币理论的发展,研究者发现除了货币的价值储藏功能外,我们还要考虑货币的其他功能,例如货币的交易功能。考虑到货币的交易功能,在一个无穷期模型中分析货币对宏观经济均衡的影响(包括通货膨胀的福利成本问题)时,大多数文献常采用以下两种范式把货币整合进模型。一条途径是假定货币持有能够给消费者带来效用,从而把货币引入效用函数(Money in the utility function,MIU);另一条途径是假设消费者购买消费品必须使用货币,从而形成预付现金约束(Cash-in-advance constrain,CIA);或者是在模型中引入交易技术,假定使用货币能带来交易时间的节约,从而形成购买-时间(shopping-time)模型。
货币引入效用函数模型(MIU)考虑到个体持有货币可以带来交易便利,节省交易成本,可以有更多的休闲,有更多的时间从事生产从而获得更多的消费品,因此实际余额的持有增加了个体的效用。当通货膨胀发生时,实际货币余额就会减少,消费者的福利就会遭受损失,于是产生福利成本。Dotsey和Ireland(1996)在一般均衡的货币模型中发现,对于美国经济,年通货膨胀率4%意味着消费者0.41%的收入损失。
在预付现金(CIA)模型中,货币并不直接进入效用函数,但假定全部或部分商品的购买必须使用现金,这种约束称为Clower约束或预付现金约束。Cooley和Hansen(1989,1991)通过把预付现金约束引入真实产业周期模型,来计算预期到了的美国通货膨胀福利成本,得出10%通货膨胀的福利成本为产出的0.38%。
在Bailey(1956)的开创性研究之后,经济学家在不同的假设基础上构造了MIU模型、CIA模型,以及购买-时间模型,也得出了不同的通货膨胀福利成本。但是这些模型所蕴涵的思想却是一致的:就是通过将真实货币持有量引入效用函数或者约束条件之中,再通过模型的最优化求解到通货膨胀率与消费者效用之间的关系。通过比较不同稳态情况下的效用水平,得到通货膨胀的福利成本:在名义利率为0的情况下,消费者效用达到最大化,考虑在某个通货膨胀率水平下,需要补贴给消费者多少比例的收入或消费,才能使其效用与最优状态下的效用水平一致。所以,需要补贴给消费者的那部分收入或者消费,就是通货膨胀的福利成本。
最后,本文利用McCallum-Goodfriend模型来计算我国1992-2008年的通货膨胀福利成本。研究发现:通货膨胀的福利成本与名义利率之间存在正相关关系;1992-2008年,我国的通货膨胀福利成本并不像我们想象中的那么大,介于GDP的0.5699%—1.8732%之间;让我们深感通胀之苦的2008年,实际的通货膨胀福利成本也只是GDP的0.8031%,约合2376.5255亿元,以全国13亿人口计算,人均福利损失约为182.8096527元;即使是这17年里通货膨胀最严重的1994年(当年的通货膨胀率达到24.1%),通货膨胀的福利成本也只有GDP的1.8199%;还有一个有意义的是,亚洲金融危机后,1998、1999年我国出现了通货紧缩,两年的通货膨胀率分别为-0.8%和-1.4%,而根据我们计算的结果,两年的通货膨胀福利成本分别占GDP的1.0941%和0.7335%,这与我们通常所认为的通货紧缩是有害的相一致,也更进一步说明了只有当名义利率为零时,社会福利才达到最大化。
为进一步验证计算的结果,我们利用Bailey(1956)的方法重新计算我国的通货膨胀福利成本。我们发现:我国的通货膨胀福利成本介于GDP的0.5635%—1.8055%之间,同样很小;Bailey(1956)方法计算的结果要比我们计算的结果小,但是差异非常微小,而且随着名义利率的增长,差异也在逐渐变大。
In 2008,the inflation caused by the spiral prices of food and petroleum became the most significant economic issue all over the world.The appeal of curbing the inflation is all around.However,is the welfare cost of inflation much? To China,which is also suffered with the inflation,how much is its welfare cost of inflation? This paper will give all the answers to these questions.
The research on the welfare cost of inflation starts with Bailey(1956),he defined the welfare cost of inflation as the area under the inverse demand function---the consumers' surplus—that could be gained by reducing the interest rate from r to zero. Lucas(2000) took advantage of Bailey's definition to calculate the cost of welfare inflation of U.S.based on time series for 1900-94.For the log-log money demand function,m_r = Ar~(-0.5),at a six percent interest rate,for example,the welfare cost is one point two percent of national income.Meanwhile,when nominal interest decreases from twelve percent to two percent,then the welfare cost will reduce by one percent of GDP.
By the development of monetary theory,researchers find out that apart from the value storage function,money also have other functions,such as trading.Considering its trading function,most literature take two patterns to integrity money into the model. One pattern is that assuming holding money can bring consumers' utility,and then include money into the utility function(MIU);and another pattern is that assuming consumer must use money to buy nonstorable goods,and then it shapes the Cash-in-advance constrain,CIA,or introduce the trading techniques into the model, assuming the use of money can bring savings of trading time,then it becomes shopping-time model.
MIU model considers money holding can bring convenient,save trading cost,then have much more time to engage in production,so money holding actually increases the utility of individual.When inflation happens,it will cause the decrease of actual money balance,the loss of consumers' welfare,and then it becomes the welfare cost. Dotsey and Ireland(1996) found in a general equilibrium money model,four percent annual inflation rate cause 0.41%consumers' income loss.
In a CIA model,money can not be put into the utility function directly.So researchers assume that part of or all of the purchase of goods must use cash,and this restriction is called Clower constrain.Cooley and Hansen(1989,1991) figured out the welfare cost of inflation in USA,finding out 10%cost of inflation welfare is 0.38%of output. After Bailey(1956)'s inaugurating research,economists construct models like MIU, CIA,and shopping-time model based on different assumptions;also elicit different welfare costs of inflation.However,the same idea lies in these models,that is,by putting the actual holding money into the utility function or restrictions and optimizing the calculation of models,we can get the relationship between the inflation rate and the consumers' utility.Comparing the levels of utility under different balance conditions,we can get the welfare cost of inflation:when nominal interest rate is zero, and the consumers' utility reach its max,considering under some inflation level,what ratio of income or consume compensation is needed to leave consumers indifferent between r and 0.As a result,the part of income or consume compensation is the welfare cost of inflation.
As last,this paper uses the Mccallum-Goodfriend framework to calculate the welfare cost of inflation,based on China time series for 1992-2008.The study shows:there exist positive correlation between the welfare cost of inflation and nominal interest rate;between those years,the welfare cost of inflation is between 0.5699%of GDP and 1.8732%of GDP,not as high as what we thought before;still in the year 2008, the actual welfare cost of inflation is 0.8031%of GDP,about RMB 237.65255 billion; The individual loss of welfare is RMB 182.8096527 based on the population of 1.3 billion;even if in 1994,when the inflation is most serious reaching 24.1%,the cost of inflation welfare is only 1.8199%of GDP;and we also find another significant thing that in 1998 and 1999 when our country appeared deflation,the inflation rate of those two years is -0.8%and -1.4%respectively,after the financial crisis in Asia,those two years' welfare cost of inflation took up of 1.0941%and 0.7335%of GDP respectively, and this also states that the deflation is harmful.Moreover,this states that only when the nominal interest rate is zero,the social welfare is optimal.
To validate the results further,we use Bailey(1956)'s method recalculation the welfare cost of inflation of our country.We find:the cost of our country is between 0.5635%and 1.8055%of GDP,the same small;the results calculated by the Bailey (1956)'s method are smaller than our results,but the difference is very little,and the difference is large gradually while the increase of nominal interest rate.
引文
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[17]McCallum,Bennett T.,and Marvin S.Goodfriend,Demand for Money:Theoretical Studies[J],in the New Palgrave:A Dictionary of Economics,ed.By John Eatwell,Murray Milgate,and Peter Newman.London:Macmillan;New York:Stockton Press,1987,775-781.
[18]Robert E.Lucas,Jr.,Inflation and Welfare[J],Econometrica,2000,68,247-274.
[19]Tobin,James,The lnterest Elasticity of the Transactions Demand for Cash[J],Reviews of Economics and Statistics,1956,38,241-247.
[20]Thomas E Cooley,and Gary D.Hansen,The lnflation Tax in a Real Business Recycle Model[J],American Economic Review,1989,79,733-748.
[21]Thomas E Cooley,and Gary D.Hansen,The Welfare Costs of Moderate Inflations[J],Journal of Money,Credit,and Banking,1991,23,483-503
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1世界经理人数据网站,http://data.icxo.com/top_bigclass_599.htm
2中国证券报,2008/08/18
3搜狐财经,http://business.sohu.com/20080617/n257540718.shtml
4世界经理人数据网站,http://data.icxo.com/htmlnews/2008/06/10/1285988-0.htm
5中国国家统计局数据,http://www.stats.gov.cn/tjsj/
6图2来自Robert E.Lucas,Jr.,lnflation and Welfare,Econometrica,2000,P254,Figure5
7表1来自Thomas F.Cooley,and Gary D.Hansen,The Inflantion Tax in a Real Business Recycle Model,American Economic Review,1989,P743,Table2
8Friedman(1969)提出了最优货币数量理论,他指出:最优货币政策应该是使得名义利率为零的平稳紧缩政策。
9图3来自Robert E.Lucas,Jr,Inflation and Welfare,Econometrica,2000,P261,Figure7
10通货膨胀数据可参见本文附录中1980-2008年的CPI走势图;利率可参见附录中1990-2007年的央行基准利率走势图。
11本节数据均来自张璐,“改革开放前通货膨胀问题研究”[J],北方经济,2008年,第2期,第58、59页
12周卫辉,“1984-1997年我国通货膨胀下的货币政策概况分析”,高校社科动态,2007年,第2期,第23页
13中国国家统计局,1978-2006年各种价格定基指数,以1978年居民消费价格指数为100,1985年为131.1,1986年为138.9,1987年为149.7,1988年为177.5
14周卫辉,“1984-1997年我国通货膨胀下的货币政策概况分析”,高校社科动态,2007年,第2期,第25页
15中国国家统计局1980-2007年《料料年国民经济和社会发展统计公报》
16同上
17周卫辉,“1984-1997年我国通货膨胀下的货币政策概况分析”,高校社科动态,2007年,第2期,第26页
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[23]龚六堂,邹恒甫,叶海云,“通货膨胀与社会福利损失”[J],《财经问题研究》,2005年,8:3-10
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[29]张璐,“改革开放前通货膨胀问题研究”[J],北方经济,2008年,2:58-59
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1世界经理人数据网站,http://data.icxo.com/top_bigclass_599.htm
2中国证券报,2008/08/18
3搜狐财经,http://business.sohu.com/20080617/n257540718.shtml
4世界经理人数据网站,http://data.icxo.com/htmlnews/2008/06/10/1285988-0.htm
5中国国家统计局数据,http://www.stats.gov.cn/tjsj/
6图2来自Robert E.Lucas,Jr.,lnflation and Welfare,Econometrica,2000,P254,Figure5
7表1来自Thomas F.Cooley,and Gary D.Hansen,The Inflantion Tax in a Real Business Recycle Model,American Economic Review,1989,P743,Table2
8Friedman(1969)提出了最优货币数量理论,他指出:最优货币政策应该是使得名义利率为零的平稳紧缩政策。
9图3来自Robert E.Lucas,Jr,Inflation and Welfare,Econometrica,2000,P261,Figure7
10通货膨胀数据可参见本文附录中1980-2008年的CPI走势图;利率可参见附录中1990-2007年的央行基准利率走势图。
11本节数据均来自张璐,“改革开放前通货膨胀问题研究”[J],北方经济,2008年,第2期,第58、59页
12周卫辉,“1984-1997年我国通货膨胀下的货币政策概况分析”,高校社科动态,2007年,第2期,第23页
13中国国家统计局,1978-2006年各种价格定基指数,以1978年居民消费价格指数为100,1985年为131.1,1986年为138.9,1987年为149.7,1988年为177.5
14周卫辉,“1984-1997年我国通货膨胀下的货币政策概况分析”,高校社科动态,2007年,第2期,第25页
15中国国家统计局1980-2007年《料料年国民经济和社会发展统计公报》
16同上
17周卫辉,“1984-1997年我国通货膨胀下的货币政策概况分析”,高校社科动态,2007年,第2期,第26页