貨幣政策對貧富不均度之影響 : 以臺灣為例 - 政大學術集成

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(1)國立政治大學社會科學院經濟學系碩士論文. 貨幣政策對貧富不均度之影響:以臺灣為例 The effect of Monetary 治on Income Inequality: 政Policy. 大. 立The case of Taiwan. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 指導教授：黃俞寧研究生：范文俞. i n U. v. 博士撰. 中華民國 106 年 7 月.

(2) 中文摘要本篇文章的目的為，在一個含有銀行信用管道以及兩種家計單位設定的動態隨機一般均衡模型的架構之中，探討中央銀行實施貨幣政策以及技術面衝擊對於貧富不均度的影響。本篇文章主要依據 Kumhof, Rancière and Winant (2015)對於兩種家計單位之設定，參考 Benigo and Eggertsson (2016)加入銀行信用管道，並參考 Lansing and Markiewicz (2016)將勞動內生化以及刻劃收入來源之不同，因而建構出一個封閉經濟體系，內含兩種不同的家計單位、商品生產部門、銀行信用管道、政府之課稅政策以及中央銀行之貨幣政策。本文發現，貧富不均度在面對. 政治大. 中央銀行實施緊縮性貨幣政策以及技術面正向衝擊時會暫時性地擴大，在長期時. 立. 會回到初始的靜態均衡值。. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. 關鍵詞:動態隨機一般均衡模型(DSGE)、貧富不均、貨幣政策. I.

(3) Abstract The main purpose of this paper is to discuss the effect of monetary policy on income inequality using a micro-based dynamic stochastic general equilibrium model with credit channel and two groups of households. Following Kumhof, Rancière and Winant (2015), households can be divided into two groups; moreover, we follow Benigo and Eggertsson (2016) to add the credit channel, and follow Lansing and Markiewicz (2016) to make households supply labor endogenously and characterize the difference of income source. Therefore, we build up a closed economy model with. 政治大 implemented by government 立and monetary policy implemented by central bank. We. two groups of households, goods firms, credit channel, the taxation policy. ‧ 國. 學. find that contractionary monetary policy and positive technology shock will temporarily generate a worse income inequality. In the long term, the economy will be. ‧. back to the initial steady state.. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. Key words: Dynamic stochastic general equilibrium (DSGE), income inequality, monetary policy. II.

(4) Contents 1. 2. 3.. Introduction .......................................................................................................... 1 Related Literature ................................................................................................ 4 Model ..................................................................................................................... 6 3.1. Labor Market ........................................................................................... 7 3.2. Households ................................................................................................ 7 3.2.1. Optimal Consumption of a Basket of Differentiated Goods .... 8 3.2.2. Top Earners .................................................................................. 8 3.2.3. Bottom Earners ............................................................................ 9 3.2.4. Measurement of Income Inequality.......................................... 10 3.3. Banks ....................................................................................................... 11 3.4. Goods Firms ........................................................................................... 12 3.5. Sticky Prices ........................................................................................... 12 3.6. Government ............................................................................................ 13 3.7. Monetary Policy ..................................................................................... 14 3.8. Marketing Clearing Conditions ............................................................ 14 Calibration .......................................................................................................... 15 Dynamic Analysis ............................................................................................... 16 5.1. The Contractionary Monetary Policy .................................................. 17 5.2. The Positive Technology Shock ............................................................. 18 Conclusion .......................................................................................................... 20 Reference ............................................................................................................ 21 Table and Figures ............................................................................................... 23. 立. ‧. ‧ 國. 學. 4. 5.. 政治大. n. al. er. io. sit. y. Nat. 6. 7. 8.. Ch. engchi. III. i n U. v.

(5) 1.. Introduction In current years, statistical data show that the growth rate of returns on. Taiwanese stock market 1 and real estates 2 are several times larger than the growth rate of labor income. 3 However, only about 18% 4 or more of Taiwanese can accumulate wealth quickly by investment. Thus, the disposable income gap between investors and workers keeps expanding. At this time, someone considers that central bank must be responsible for improvement in income inequality when stabilizing the GDP growth rate. As a result, we wonder whether monetary policy can slow down the. 政治大 Kumhof, Rancière and 立Winant (2015), and Kumhof and Rancière (2010) find. deterioration of income inequality.. ‧ 國. 學. that a sharp increase in income inequality and debt-to-income ratios among lowerand middle-income households caused subprime mortgage crisis, and then led to. ‧. financial crisis in 2008 causing global recession. Taking Taiwan for example, the GDP. sit. y. Nat. growth rate in 2008 declined to 0.73%; moreover, it declined to -1.81% in 2009. In. n. al. er. io. addition, firms started to let employers take unpaid leave or even lay off them. As a. i n U. v. result, the lower income share of the low- or middle-income groups not only increased. Ch. engchi. the debt-to-income ratios, but worsened the solvency of the low- and middle-income groups to become a potential factor of another financial crisis. Therefore, more and more researches focus on income inequality.. 1. The raw data are available in Taiwan Economic Journal Database. We take the average of data from. 2003 to 2016. 2. The raw data are available in Sinyi Realty Incorporation. We take the average of data from 2001 to. 2016. 3. The raw data are available in the Directorate-General of Budget, Accounting and Statistics, Executive. Yuan of Taiwan. We take the average of data from 2012 to 2016. 4. The raw data are available in the Directorate-General of Budget, Accounting and Statistics, Executive. Yuan of Taiwan. We take the average of data from 2011 to 2015. 1.

(6) The empirical works on income inequality of Taiwan have traditionally focused on the Gini coefficient or the Oshima index. 5 These two indexes both show that the income distribution of Taiwan becomes more and more uneven. Especially, in 2001 and 2009, the Oshima index rises sharply during the Dot-com bubble and the financial crisis. Therefore, we can find that the economic crises will deteriorate the income distribution of Taiwan. Moreover, Chu and Kang (2015) calculates the ratio of Taiwanese income of top 5% over bottom 5%. The increasing trend of income inequality is more obvious than Oshima index and Gini coefficient.. 立. 4.00. Nat. 4.50. y. 5.00. ‧. 5.50. 0.36 0.34 0.32 0.30 0.28 0.26 0.24 0.22 0.20. er. io. sit. 6.00. ‧ 國. 6.50. 學. 7.00. 政治大. n. Gini coefficientv a l Oshima index i n Ch i UArea (June 2017) e n g cinhTaiwan Source: The Survey of Family Income and Expenditure 6. Figure 1: Taiwanese Oshima index and Gini coefficient from 1990-2014. 5. The Oshima index is defined as the ratio of income of top 20% over that of bottom 20%. The Directorate-General of Budget, Accounting and Statistics, Executive Yuan of Taiwan and the Ministry of Finance updates annually. 6 The Directorate-General of Budget, Accounting and Statistics, Executive Yuan of Taiwan surveys the residence’s income annually. The outcome can be used to calculate Oshima index and Gini coefficient. 2.

(7) 93.39 96.56. 100 80 60 40. 32.74. 42.96 46.21 37.27 40.48. 65.97 58.61 62.09 54.81 51.33. 74.95. 20 0. Source: Chu and Kang (2015). Figure 2: The ratio of Taiwanese income of top 5% over bottom 5% from 1998-2011 30% 28% 26%. 立. 24% 22%. 16%. ‧. 14%. ‧ 國. 18%. 學. 20%. 政治大. y. Nat. sit. Source: Chu, Chou and Hu (2015). n. al. er. io. Figure 3: Taiwanese top 10% income shares from 2001-2013. Ch. engchi. i n U. v. Recent empirical works have also emphasized the income share of the rich. For example, Chu, Chou and Hu (2015) estimates that the top 10% richer almost hold 25% or 26% of Taiwan total income. In most of traditional macroeconomic theoretical model, there is only one representative household, but it is hard to discuss income inequality under this assumption. Therefore, the heterogeneity of households plays a key role in our paper. Referring to Kumhof, Rancière and Winant (2015), Kumhof, Lebarz, Rancière, Richter and Throckmorton (2012), and Lansing and Markiewicz (2016), we assume the top 10% of the income distribution can be considered as savers or entrepreneurs 3.

(8) implying top earners can use parts of income to accumulate wealth in the form of deposits in banks. On the other hand, the bottom 90% earners of the income distribution can be considered as debtors or workers implying bottom earners can smooth the variation of their consumption credited from banks, but probably be along with a higher debt-to-income ratio. Different from Kumhof, Rancière and Winant (2015), Kumhof, Lebarz, Rancière, Richter and Throckmorton (2012), and Lansing and Markiewicz (2016), we assume both groups of households supply labor endogenously to firms, add the existence of banks that can transfer top earners’ wealth. 政治大. to bottom earners with two kinds of interest rates, and add the price setting to test the effects of policy.. 立. As a result, we present a dynamic stochastic general equilibrium model with two. ‧ 國. 學. kinds of households to explain whether or not positive technology shock and. ‧. contractionary monetary policy will lead to a worse income inequality.. sit. y. Nat. This paper is divided into eight chapters. Chapter one is the introduction. Chapter. io. er. two lists the related literatures. Chapter three outlines the DSGE model, the first-order conditions, taxation policy and central bank’s monetary policy. Chapter four discusses. al. n. v i n model calibration. Chapter five C shows the simulation of h e n g c h i Uthe model by Dynare. Chapter. six concludes the outcomes. Chapter seven is the reference. Chapter eight shows the table of parameters and the figures of dynamic analyses.. 2.. Related Literature Kumhof, Rancière and Winant (2015) builds up an endowment two-agent closed. economic model by setting different endowment wealth. They assume top earners and bottom earners as savers and borrowers respectively. In this framework, they explain the relationship among the income inequality, debt leverage and default decision. 4.

(9) Furthermore, they find that the debt leverage and the probability of default rise endogenously7 if the income distribution becomes more uneven. Lansing and Markiewicz (2016) builds up a two-agent general equilibrium model by setting different wealth and income. They assume top earners and bottom earners as capital owners and workers respectively. In their framework, they prove that the capital owners can always benefit from the technology change, but only when specific conditions are conformed together, the workers can benefit from the technology change. They also explore that the variations of income inequality, consumption. 政治大 Rancière, Throckmorton, Kumhof, Lebarz and Richter (2012) builds up a 立. inequality under perfect foresight, myopic exceptions and learning.. two-agent open economic model by setting different endowment wealth. They prove. ‧ 國. 學. that in the developed economies the increase in income inequality will cause worse. ‧. current account deficits while in the emerging markets will cause current account. sit. y. Nat. surpluses instead. They also find that financial liberalization can alleviate the effect of. io. deficits.. er. income inequality but will cause higher household debt and larger current account. al. n. v i n Motta and Tirelli (2014) C builds up a two-agentUmodel to discuss the relation hengchi. between the limited asset market participation and income distribution. In their. framework, there are two types of households: one is Ricardian households who can participate in financial market, and the other is rule-of-thumb households who don’t have access to enter financial market and don’t hold any wealth. In their framework, they find that the less asset market participation will generate a worse state of consumption inequality and income inequality, and thus will generate a higher macroeconomic volatility. Besides, they prove that redistributive policies targeting 7. They assume bottom earners choose whether to default rationally and endogenously. But doing default will bring bottom earners large output losses and utility losses. 5.

(10) consumption inequality will help macro-economy stable. García-Peñalosa and Turnovsky (2013) builds up a heterogeneous-agent Ramsey model to find what causes income mobility and inequality. In their model, households are with different initial wealth and ability (labor endowment). They think labor supply decisions may have an equalizing and unequalizing effect, so they prove that both an increase and a decrease in overall income inequality can cause higher income mobility Ravenna and Vincent (2014) builds up a two-agent model to compare the income. 政治大 cross-sectional tax reallocation. In their framework, different technologies are the 立. inequality driven by cross-sectional differential productivity growth and driven by. result of labor supplied by different type of households. They find that cross-sectional. ‧ 國. 學. productivity growth generates much less divergence between income and. y. sit. io. n. al. er. Model. Nat. 3.. ‧. consumption than cross-sectional tax allocation.. i n U. v. Following Kumhof, Rancière and Winant (2015), Lansing and Markiewicz. Ch. engchi. (2016), and Benigo and Eggertsson (2016), 8 we set up a closed-economy model consisting of two groups of households (top earners and bottom earners), monopolistically competitive firms, competitive banks, government and central bank. Labor market is assumed to be perfectly competitive. Firms use labors as inputs to produce goods. Banks make loans to the bottom earners and accept the deposits from top earners. Both firms and banks are owned by top earners. Government redistributes income from top earners to bottom earners via a business tax on firms and banks. Central bank sets up monetary policy to control the interest rate on deposits. 8. They set up a simple endowment model consisting of savers, borrowers and banks. 6.

(11) In order to distinguish activities of households, we make exclusive activities of top earners with the superscript T , and make exclusive activities of bottom earners with the superscript B .. 3.1. Labor Market We assume that every labor is identical for firms, so each top earner and bottom T. B. earner supply the same type of labor, denoted nt , nt respectively, for the same nominal wage per labor, denoted. Wt . In the equilibrium, the labor demand of firm i ,. 政治大. denoted N t ( i ) , must be equal to the sum of labor supply from top earners and from. 立. bottom earners.. ‧ 國. 學. N t= ( i ) χ ntT ( i ) + (1 − χ ) ntB ( i ). (1). Moreover, the total labor market equilibrium can be written as. ‧. (2). n. al. er. io. sit. y. Nat. 3.2. Households. N t= χ ntT + (1 − χ ) ntB. i n U. v. We assume that in this economy there is a continuum of households with mass. Ch. engchi. one, divided into two groups: one is top earners, with population share. χ ( 0 < χ < 1) , and the other is bottom earners, with population share (1 − χ ) . In this paper, we take the case χ = 10% as the benchmark. Hence, top earners and bottom earners can correspond to the top 10% and bottom 90% of the income distribution respectively. In our model, heterogeneity depends on sources of income and different initial wealth, 9 so we assume that top earners are not only the owners of firms and banks but 9. In reality, both kinds of households can deposit or apply loans. We consider that the total amount of. deposits is larger than of loans for top earners. 7.

(12) also the depositors of banks; on the other hand, bottom earners are the debtors of banks. Heterogeneity in subjective discount factors, a common assumption in literatures, can be easily represented.. 3.2.1. Optimal Consumption of a Basket of Differentiated Goods Before dealing with the households’ optimal consumption, we have to find the optimal consumption basket, given any level of consumption expenditures. In this j case, we set the consumption of agent j (where j = T or B ) from firm i as ct ( i ). ∫ P ( i ) c ( i ) di ≡ Z 政治大 the optimal basket of consumption 立 problem can be written as 1. and set a given level of consumption expenditures as. 0. j. t. t. ε. ‧ 國. ‧. 1. 0. (3). y. (4). io. to (4), we can get the demand function for firm i :. n. al. sit. is the elasticity of substitution. Through maximizing equation (3) subject. er. ε. s.t. ∫ Pt ( i ) ctj ( i ) di = Z t j. Nat. where. . Therefore,. 學. ε −1  1 j  ε −1 ε di c i max ( ) ( )   ∫ t ctj ( i )  0 . j t. Cctjh( i ) =  Pt ( i )  ctj U n i e n gPt c h i −ε. v. (5). 3.2.2. Top Earners The utility function of the representative top earner can be written as T 1+ϕ    T ( nt )  U t Et ∑ βT ln ct − =  1+ ϕ  t =1   ∞. t. (6) 10. where ct represents top earners’ per capita real consumption, ϕ is the inverse T. 10. In Kumhof, Rancière and Winant (2015), financial wealth enters top earners’ utility function. 8.

(13) labor supply elasticity, and. βT. is the subjective discount factor for the top earners. ( 0 < βT < 1) . The budget constraint of each top earner is given by ctT=. Wt T (1 + it −1 ) Dt −1 Dt 1  ∏tfirms ∏banks TAX t  − +  + t − nt +  πt χ χ  Pt Pt −1 Pt Pt  χ. (7). where Dt represents the amount of top earners’ per capita nominal deposits accepted in period. t and will be repaid with the interest rate on deposits ( it ) in period t + 1 .. The inflation rate is. ∏. banks t. π t ≡ Pt Pt −1 . ∏tfirms. is the profits of firms in period. 治政 is the banks’ profits in period t . Both ∏ 大and 立 firms t. t , and. ∏banks are exogenous t. ‧ 國. 學. for top earners. TAX t is the business tax which will be transferred to bottom earners as subsidies. We denote wt. ≡ Wt Pt , dt ≡ Dt Pt , and rt ≡ Et (1 + it ) π t +1 − 1 .. ‧. Top earners maximize (6) subject to (7). Thus the F.O.Cs of top earners can be. n. al. hTe nT gϕ c h i U ct ( nt. ). = wt. er. io. −1.  cT  1 Et βT  t T+1  = 1 + rt c C  t . sit. y. Nat. simplified to. v ni. (8). (9). The equation (8) is the standard intertemporal Euler equation of top earners. The equation (9) indicates top earners’ tradeoff between the consumption and labor supply.. 3.2.3. Bottom Earners Bottom earners’ utility takes the same functional form, so the utility function of the representative bottom earner can be written as. 9.

(14) B 1+ϕ   n ( )  t  Vt Et ∑ β B t ln ctB − =  1+ ϕ  t =1   ∞. (10). B. where ct represents bottom earners’ per capita real consumption, and subjective discount factor for the bottom earners. βB. is the. ( 0 < β B < 1) . The budget constraint. of each bottom earner is given by Wt B (1 + it −1 ) Lt −1 Lt 1  TAX t  + +  nt −  πt Pt Pt −1 Pt Pt  1 − χ  B. B c= t. (11). where Lt represents the amount of bottom earners’ per capita nominal loans credited. 治政 and should be repaid with the 大interest rate on loans ( i 立. B t. t. from banks in period. ) in. lt ≡ Lt Pt , and rt B ≡ Et (1 + itB ) π t +1 − 1 .. ‧ 國. 學. period t + 1 . We denote. Bottom earners maximize (10) subject to (11). Thus the F.O.Cs of bottom earners. ‧. can be simplified to. −1. n. ctB ( ntB ) = wt ϕ. Ch. engchi. y. sit. io. al. (12). er. Nat.  cB  1 Et βT  t +B1  = B  ct  1 + rt. i n U. v. (13). The equation (12) is the standard intertemporal Euler equation of bottom earners. The equation (13) indicates bottom earners’ tradeoff between the consumption and labor supply.. 3.2.4. Measurement of Income Inequality In this paper, we characterize income inequality mainly by the top earners’ income share instead of Gini efficient or Oshima index. The top earners’ income share after tax, denoted. τ t , can be written as 10.

(15)  T TAX t   1  ∏tfirms ∏banks + t − χ  wt nt + (1 + rt −1 ) dt −1 +   χ χ   Pt  χ  τt = .  T TAX t   1  ∏tfirms ∏banks B t + − χ  wt nt + (1 + rt −1 ) dt −1 +    + (1 − χ ) wt nt +TAX t χ χ χ P  t  . 3.3. Banks We assume that anyone can’t borrow from others directly, so banks serve as financial intermediates transferring the deposits to someone in need. Besides, compared with individuals, we think that the intermediaries have more information to. 政治大 amount of deposits and loans should be issued. 立. distinguish ex ante who among the debtors will default or not 11 and how much. To simplify the model, we assume banks are one-period-lived, 12 and every. ‧ 國. 學. period new banks will be set up without any limit. The main goal of banks is to BK. BK. ‧. choose the optimal amount of deposits, denoted Dt , and loans, denoted Lt , to. y max (1 + itB ) LBK − (1 + it ) DtBK − Ζt  t. io. DtBK , LtBK. n. al. er. = ∏tBank +1. sit. Nat. maximize the profit..  = Ζt α  LBK where t. 2. and accepting deposits.. 2 + α  DtBK . Ch. 2. i n U. (14). v. 2 is the adjustment cost of making loans,. engchi. The budget constraint is given by BK LBK t = Dt. (15). which is the balance sheet of the bank during period t , i.e. all the deposits are used to BK. make loans to bottom earners. We denote lt. 11 12. ≡ LBK Pt , dtBK ≡ DtBK Pt and t. Therefore, we assume all bottom earners won’t default on their past loans. According to Heuvel (2008), if there is no adjustment costs problems, nor agency optimizing. problems between banks and others, the setting is without loss of generality. 11.

(16) = ζ t α ltBK . 2. 2. 2 + α  dtBK . 2.. After (14), (15) are represented in the real term, banks maximize (14) subject to (15). The optimal condition can be represented as below.. (1 + r ) − (1 + r ) ≈ ( 2α ) d B. t. t. BK t. = ( 2α ) ltBK .. (16). The equation (16) indicates the relationship between the spread and the amount of loans (deposits).. 3.4. Goods Firms. 政治大. We assume that in this economy there is a continuum of firms with mass one.. 立. 學. Yt ( i ) = e At N t ( i ). represents the level of technology where. At follows an exogenous stochastic. y. sit. io. A=t ρ A At −1 + ε A,t , 0 < ρ A < 1. (18). n. er. Nat. autoregressive process below.. al. (17). ‧. e At. ‧ 國. The production function of the representative firm i is given by. where ρ A is the autocorrelation of technology and. Ch. v. ε A,t nisi a white noise.. engchi U. The first-order condition for goods firms can be written as. MCtr =. Wt 1 W 1 = t At . Pt MPN t Pt e. (19). 3.5. Sticky Prices *. Under Calvo’s pricing, each firm can reoptimize and set the price Pt with the probability (1 − θ ) in the beginning of every period. Therefore, the firm’s profit. 12.

(17) maximization problem can be written as ∞. (. ). (20).  Pt*   Pt*  ≈ Et   ct + k ≈ Et   ct + k  Pt + k   Pt + k . (21). θ k Et  Λ t ,t + k Pt* yt + k |t − TCtn+ k |t ( yt + k |t )  max ∑ *   Pt k =0 −ε. s.t. Et yt + k |t. where Λ t ,t + k. −ε. −1 −1 T B  Pt Pt  k  ct + k  k  ct + k   is the weighted ≡ Et  χβT  T  + (1 − χ ) β B  B    ct  Pt + k  ct  Pt + k . T B discount factor, and ct + k ≡ χ ct + k + (1 − χ ) ct + k is the total consumption of households.. 政治大. *. Finally, we can get the optimal price-setting condition, denoted Pt :. ε −1. Et. k =0. Λ t ,t + k Pt + k ε ct + k MCtr+ k |t. ∞. ∑θ. k. k =0. Λ t + k |t Pt + k. ε −1. ct + k. And the price level can be described by the equation 1−ε.  P*  = θ + (1 − θ )  t   Pt −1 . io. Therefore, the sum of firms’ profits can be written as. al. n. v i n di θ Pi y U + 1−θ P = ∫  P ( i ) y ( i ) − WC (hi ) eN n( i )g ch ( ). ∏tfirms =. 1. 0. t. t. *. t. t. t. (23). er. Nat. πt. 1−ε. (22). y. ε. k. ‧. ‧ 國. ∑θ. 學. Pt * ≈. ∞. sit. 立. t. y − Wt Nt. t −1 t. (24). 3.6. Government Government levies a business tax on firms’ and banks’ profits: TAX = γ Tax ( Π tfirms + Π banks ) t t. where. (25). γ Tax is the business tax rate. The taxes will be transferred to each bottom. earner as subsidies.. 13.

(18) 3.7. Monetary Policy In this model, the central bank follows the Taylor’s rule: ρy. ρ. 1 + it  π t  π  yt  γ mp ,t =    e 1+ i  π   y . (26). = γ mp ,t ρ mpγ mp ,t −1 + ε mp ,t. (27). where i is the steady state value of the nominal interest rate on deposits, ρi is autocorrelation of the interest rate on deposits, ρπ is autocorrelation of inflation gap,. 政治大. ρ y is autocorrelation of output gap while ρπ > 1 , ρ y < 1 , and ε mp ,t is the monetary. 立. ‧ 國. ε mp ,t is positive, it represents that the. 學. policy shock which is a white noise. When. central bank implements a contractionary monetary policy and vice versa.. ‧ sit. y. Nat. 3.8. Marketing Clearing Conditions. n. al. er. io. In the equilibrium, the demand and supply of loans and deposits match, the. i n U. v. amount of deposits equals the amount of loans, the total output equals total. Ch. engchi. consumption plus adjustment cost, and the total labor supply matches the labor demand.. ltBK=. (1 − χ ) lt. (28). dtBK = χ dt. (29). yt= χ ctT + (1 − χ ) ctB + ζ t. (30). N t= χ ntT + (1 − χ ) ntB. (31). 14.

(19) 4.. Calibration In this paper, we follow Kumhof, Rancière and Winant (2015) to set parameters.. In Kumhof, Rancière and Winant (2015), the parameters are calibrated for the data of U.S.A to match key features of U.S.A economy. The parameters in this paper are listed in table 1 and are calibrated for the data of Taiwan. The steady state interest rate on deposits is fixed at 0.00259 per quarter, calibrated for the one-year interest rate on deposits of Taiwanese five major banks, 13ˑ 14 by fixing top earners’ subjective discount factor at βT = 0.997418 . The. 政治大. steady state interest rate on loans is fixed at 0.00644 per quarter, calibrated for the. 立. interest rate on one-year consumer loans of Taiwanese five major banks, 15 by fixing. ‧ 國. 學. bottom earners’ subjective discount factor at β B = 0.993601 .. ‧. Following Hwang (2013), we set the inverse labor supply elasticity ϕ at 1.. y. Nat. Similar to values typically used in literatures, we set the steady state price at 1 and the. al. er. io. sit. markup ε ( ε − 1) at 1.25 by fixing the elasticity of substitution at 5.. v. n. We calibrate the initial steady state values of the saving ratio s and the top. C h υ to be equal engchi. earners’ income share before tax. i n U. to the empirical evidences of. counterparts. In this model, s is given by s=. and 13. υ. d 1  ∏ firms ∏banks  T wn + (1 + i ) d +  + χ  P χ. is given by. Taiwanese five major banks conclude Bank of Taiwan, Taiwan Cooperative Bank, First Bank, Hua. Nan Bank, and Land Bank of Taiwan. 14. The raw data are available in Central Bank of Taiwan. https://goo.gl/A7XLz6 .. 15. The raw data are available in Central Bank of Taiwan. https://goo.gl/ninHt3 . We take the average of. data from 2010 to 2016. 15.

(20)  T 1  ∏ firms ∏banks   χ  wn + (1 + i ) d +  +  P χ χ    υ= .  T 1  ∏ firms ∏banks   B + χ  wn + (1 + i ) d +    + (1 − χ ) wn P χ χ    To calibrate the value of. s , we use the data average, 16 which equals 20.8735%,. calculated by the Directorate-General of Budget, Accounting and Statistics, Executive Yuan of Taiwan. To calibrate the value of. υ,. we use the 2009-2015 data average,. which equals 25.93%, estimated by Chu, Chou, and Hu (2015). Therefore, we set. α. fixed at 0.035 to approximate these key features.. 政治大 Moyen and Stahler (2010),立 we set autocorrelation of technology, nominal interest rate Referring to Hwang (2013), Adam (2011), Ortega and Rebei (2006), and Mayer,. ‧. ‧ 國. 0.01 and 0.3.. 學. on deposits, inflation rate gap, output gap and monetary policy shock at 0.9, 0.6, 1.5,. Pursuant to Article 10 of R.O.C. Value-added and Non-value-added Business Tax. sit. y. Nat. Act, the business tax rate shall be no less than 5% and no more 10%. Therefore, we. n. al. er. io. set the business tax rate at 5%.. 5.. Dynamic Analysis. Ch. engchi. i n U. v. In this chapter, the case the population share of top earners. χ equals 0.1 is the. benchmark indicated by the solid line. First, we will discuss how our model works when facing two kinds of exogenous shocks: contractionary monetary policy shock and positive technology shock. Secondly, we will compare with the case that 16. χ is 0.2 indicated by the dash line.. The raw data are available in “The Survey of Family Income and Expenditure” conducted by the. Directorate-General of Budget, Accounting and Statistics, Executive Yuan of Taiwan. https://goo.gl/kwWxo7 . We take the average of data from 2012 to 2016. 16.

(21) 5.1. The Contractionary Monetary Policy Figure 4 shows an 1% deviation contractionary monetary policy to the interest rate on deposits it . The implementation of the contractionary monetary policy means that the central bank wants banks to accept more deposits, and thus demand of deposits rises. According to the Taylor’s rule, the contractionary monetary policy will generate an increase in the interest rate on deposits and a decrease in the output and inflation rate. The lower output means that firms decrease the labor demand, and thus the equilibrium employment and wage decline. Due to the price rigidity, the decline of. 政治大. the wage is faster than the adjustment of the price, the firms’ profits will increase. 立. temporarily.. ‧ 國. 學. The decline of the labor income forces bottom earners to apply more loans from banks to smooth the drop in the consumption, so the interest rate on loans increases.. ‧. The higher interest rate on deposits will also induce top earners to delay their. sit. y. Nat. consumption to deposit more. The amount of banks’ profits is quite small, so we. n. al. er. io. ignore the effect of the variation of banks’ profits.. i n U. v. In the first several periods, even though demand of deposits subsequently. Ch. engchi. decreases back to the steady state, supply of deposits still increases resulted from the increase in returns on deposits and firms’ profits. On the other hand, in order to meet the balance, banks will decrease the interest rate on loans to induce bottom earners to borrow more. Thus the interest rate on deposits and loans both decrease gradually. Hereafter, due to the persistence of this policy, supply and demand of deposits decrease, and the labor income increases. Subsequently, demand and supply of loans decrease. Therefore, the interest rate on deposits and loans keep decreasing back to the steady state values. As a result, we can see that the amount of deposits and loans increase last almost 3 periods, with a subsequent decrease. Profits of banks, followed 17.

(22) by the variations of the amount of deposits and loans, increase in the first several periods and then decrease back to steady state values. In our model, the increase in firms’ profits is enough to offset the effect of increasing in interest rate on deposits, 17 so top earners still can consume more while bottom earners have to smooth the drop of consumption by applying more loans. In summary, the income share of top earners will increase in the first several periods and then decreases back to the steady state because of the variations of deposits and profits of firms. Comparing with the dash line, the variations in case χ = 0.2 are smoother. We. 政治大 consider the main reason is that the population share of top earners doubles. So banks 立 will accept less deposits from the individual top earner, and profits of firms, banks. ‧ 國. 學. will be shared by more people. Therefore, the variations of top earners’ consumption,. ‧. the amount of deposits and profits of firms, banks become smooth obviously. But the. y. sit. io. n. al. er. previous case.. Nat. variations of bottom earners’ consumption, the amount of loans are similar to the. 5.2. The Positive Technology Shock. Ch. engchi. i n U. v. Figure 5 shows an 1% deviation positive shock to technology At . This shock allows labors to become more productivity, and thus the wage increases. However, given the values of parameters above, firms will be able to increase their outputs and profits with fewer labors. 18 In addition, this shock also allows some firms to decline their price to maximize their profits, and thus price level, inflation rate decline. On the 17. In the steady state equilibrium, the top earners’ income is composed of firms’ profits by almost 67%,. deposits with interest rate by almost 20.9%, and labor income by almost 11.67% 18. According to Galí, J. (2015), the sign of the response of employment to a positive technology shock. depends on the values of parameters. 18.

(23) other hand, although the employment decreases, the labor income of top earners and bottom earners still increase. When labor income and firms’ profits increase, top earners will be able to simultaneously consume and deposit more. Along with the increase of the amount of deposits supplied, the interest rate on deposits will decline. Whereas the balance sheet, banks would like to lower down the interest rate on loans to induce bottom earners to borrow more. In the first several periods, the solvency of bottom earners can be improved with higher labor income, so demand of loans increases. In other words, demand of. 政治大 rise gradually. Hereafter, due to the persistent of technology shock, supply of deposits 立. deposits will increase. Thus the interest rate on loans and the interest rate on deposits. and demand of loans decrease. In other words, supply of loans and demand of. ‧ 國. 學. deposits will decrease. Consequently, we can find the interest rate on loans and the. ‧. interest rate on deposits keep rising until returning the steady state values, and the. sit. y. Nat. amount of deposits and loans increase last almost 10 periods, with a subsequent. io. er. increases back to their steady state values. Profits of banks, followed by the variations of the amount of deposits and loans, increase in the first several periods and then. al. n. v i n C h Hence, we can find decrease back to steady state values. that the consumptions of top engchi U earners and bottom earners will increase.. In summary, the income share of top earners will increase in the first several periods and then decreases back to the steady state because of the variations of deposits and profits of firms and banks. Comparing with the dash line, the variations of top earners’ consumption, the amount of deposits, and profits of firms become smooth in the case same reason in the previous dynamic analysis.. 19. χ is 0.2 for the.

(24) 6.. Conclusion This paper presents a theoretical framework calibrated for the data of Taiwan. We. explore the nexus between the exogenous shocks and income inequality. In our model, the substantial assumption is that firms’ profits belong to the top earners. 19 This assumption not only affects the optimization decisions of the top earners significantly but generates income inequality from the bottom earners. Therefore, some responses to exogenous shocks are a little different from traditional theoretical models. There are two main outcomes: one is that contractionary monetary policy will. 政治大 that positive technology shock 立 will also generate a worse income inequality, due to. generate a worse income inequality, due to the increase in profits of firms, the other is. ‧ 國. 學. the increase in profits of firms and labor income.. Three shortcomings of our model are in order. First, our framework does not. ‧. allow the dynamic change of income statuses. Second, income inequality resulted. sit. y. Nat. from the default crises can’t be explained. So we can’t completely analysis the. n. al. er. io. variation of income inequality during the Dot-com bubble or the financial crisis. Third,. i n U. v. in reality, most of entrepreneurs tend to invest in real estates or stock market rather. Ch. engchi. than to deposit with a relatively lower return.. 19. Most literatures assume the firms’ profits don’t belong to households or just equal 0. So the response of and the influence of firms’ profits are often ignored. 20.

(25) 7.. Reference. 黃俞寧，2013，動態隨機一般均衡架構在臺灣貨幣政策制定上之應用，中央銀行季刊 35，3-34 Adam, K. (2011). “Government debt and optimal policy.” European Economic Review, 55(1), 57-74.. monetary and. fiscal. Benigno, P., Eggertsson, G., & Romei, F. (2016). “Dynamic Debt Deleveraging and Optimal Monetary Policy” (No. 11180). CEPR Discussion Papers. Chu, C., T. Chow, & S-C. Hu (2015). “Top Income Shares in Taiwan 1977-2013.” WTID Working Paper 2015/2.. 立. 政治大. ‧ 國. 學. Chu, C. C., & Kang, T. Y. (2015). “SOCIAL INEQUALITIES DURING ECONOMIC TRANSFORMATION.” Taiwan Economic Forecast and Policy, 45(2), 1.. ‧. Galí, J. (2015). “Monetary policy, inflation, and the business cycle: an introduction to the new Keynesian framework and its applications.” Princeton University Press.. y. Nat. sit. n. al. er. io. García-Peñalosa, C., & Turnovsky, S. J. (2015). “Income inequality, mobility, and the accumulation of capital.” Macroeconomic Dynamics, 19(06), 1332-1357.. Ch. i n U. v. Kumhof, M., & Rancière, R. G. (2010). “Inequality, leverage and crises.” Working Paper 10/268, IMF November 2010.. engchi. Kumhof, M., Rancière, R., & Winant, P. (2015). “Inequality, leverage, and crises.” The American Economic Review, 105(3), 1217-1245. Lansing, K. J., & Markiewicz, A. (2016). “Top incomes, rising inequality, and welfare.” The Economic Journal, 26 April 2017. Mayer, E., Moyen, S., Stahler, N. (2010), “Government expenditures and unemployment: a DSGE perspective.” Discussion paper/Deutsche Bundesbank/Series 1, Economic studies 18/2010.. 21.

(26) Motta, G. E., & Tirelli, P. (2013). “Limited asset market participation, income inequality and macroeconomic volatility.” University of Milan Bicocca Department of Economics, Management and Statistics Working Paper No. 261 Ortega E. and N. Rebei. (2006). “The Welfare Implications of Inflation versus Price-Level Targeting in a Two-Sector, Small Open Economy.” Bank of Canada Working Paper No. 2006–12. Rancière, R., Throckmorton, M. N. A., Kumhof, M. M., Lebarz, M. C., & Richter, M. A. W. (2012). “Income inequality and current account imbalances” (No. 12-18). International Monetary Fund. Ravenna, F., & Vincent, N. (2014). “Inequality and debt in a model with heterogeneous agents.” Economics Letters, 123(2), 177-182.. 立. 政治大. ‧ 國. 學. Teo, W. L. (2011). “Inventories and optimal monetary policy in a small open economy.” Journal of International Money and Finance, 30(8), 1719-1748.. ‧. Van den Heuvel, S. J. (2008). “The welfare cost of requirements.” Journal of Monetary Economics, 55(2), 298-320.. n. er. io. sit. y. Nat. al. Ch. engchi. 22. i n U. v. bank. capital.

(27) 8.. Table and Figures Table 1: Calibration Parameters. Parameter. Description. Implied Values. βT. The subjective discount factor for top earners. 0.997418. βB. The subjective discount factor for bottom earners. 0.993601. χ. The population share of top earners. 0.1. ε. The elasticity of substitution. ϕ. The inverse labor supply elasticity. ‧ 國. 0.035. The probability of firms to maintain the prices. 0.75. y. The coefficient of the banks’ adjustment cost. ‧. 0.05. The business tax rate. sit. γ Tax. 1. Nat. θ. 5. 學. α. 立. 政治大. n. al. er. io. Shock parameter-persistence. v. ρA. The autocorrelation of technology. ρi. The autocorrelation of the interest rate on deposits. 0.6. ρπ. The autocorrelation of inflation gap. 1.5. ρy. The autocorrelation of output gap. 0.01. ρ mp. The autocorrelation of monetary policy shock. 0.3. Ch. engchi. 23. i n U. 0.9.

(28) 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. Figure 4: The Impulse responses to Contractionary Monetary Policy (Deviation from Steady State). 24.

(29) 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. Figure 5: The Impulse Responses to Positive Technology Shock (Deviation from Steady State). 25.

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