ESSAYS ON PRICE-SETTING MODELS AND INFLATION DYNAMICS

Transcription

1 ESSAYS ON PRICE-SETTING MODELS AND INFLATION DYNAMICS DISSERTATION Presented in Partial Ful llment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Bae-Geun Kim, M.A. * * * * * The Ohio State University 27 Dissertation Committee: Approved by William Dupor, Adviser Paul Evans J. Huston McCulloch Adviser Graduate Program in Economics

2 c Copyright by Bae-Geun Kim 27

3 ABSTRACT This dissertation investigates the empirical validity of several theories on rms price-setting behavior and the dynamics of in ation. The dissertation consists of two essays. The rst essay, Reassessment of the New Keynesian Phillips Curve: Gross vs. Value-Added Price In ation, reexamines the new Keynesian Phillips curve based on the distinction between gross price and value-added price in ation. It is shown that a standard new Keynesian Phillips curve can be interpreted as describing the behavior of gross price in ation and, therefore, it is essential to incorporate intermediate input costs in constructing marginal cost measures. Moreover, from this gross price in ation model, the valued-added price in ation model is derived explicitly, in which the real price of intermediate inputs plays an important role. The new Keynesian Phillips curve is tested using both in ation models. Our results show that (1) the evidence for the new Keynesian Phillips curve is weak for the whole sample period regardless of model speci cation; (2) in some subsamples, however, especially during high and volatile in ation periods, the evidence becomes stronger for the value-added price in ation model; and (3) the e ects on in ation of the real intermediate input prices and the backward-looking behavior of economic agents are substantial. The second essay, The Empirical Relationship between the Markup, Marginal Cost and In ation, and Its Implications for Price-Setting Models, studies how in ation ii

4 responds di erently to di erent types of structural shocks. For this purpose, a structural vector autoregression model is constructed that can identify the e ects of shocks to the desired markup, technology and aggregate demand. The model shows that (1) in ation responds immediately to shocks to the desired markup and technology whereas it displays a hump-shaped response to a demand shock; and (2) the gradual response of in ation to a demand shock is caused by an inertial response of marginal cost, not by an inertial response of in ation to changes in marginal cost. These empirical ndings imply that in ation itself does not exhibit intrinsic inertia, and thus some sticky price models need not be discarded simply because they fail to generate the hump-shaped response of in ation to a demand shock. The analyses suggest that the reason for the gradual response of in ation to a demand shock should be found by examining elements that a ect production cost. iii

5 To my wife and two daughters, Si-Yeon and Gyu-Yeon iv

6 ACKNOWLEDGMENTS The road to this dissertation was not an easy task. Sometimes it was lled with excitement. In other times, I was confronted with big obstacles. Each time I had a hardship without knowing where to go, my adviser, William Dupor, suggested great ideas and gave me encouragements. Discussions with him led me to new ways of solving the problems. Professor Paul Evans gave me invaluable advices and insights as well as a vast amount of information. I was always deeply impressed by his comments on my drafts that lled the margin of the papers. Professor J. Huston McCulloch provided me with di erent perspectives, which later helped me greatly to improve my papers. Without the help of these professors, my achievement so far would not have been possible. I thank Professors Pok-sang Lam and Masao Ogaki who provided wonderful teaching during the rst and second years of my academic life. The materials in their courses became the workhorses in my research projects. I am also grateful for nancial support from the Department of Economics at the Ohio State University in the form of Graduate Teaching Associateship. Without the support, I would not have made it this far. I wish to express my deepest appreciation to my family. My wife, Hye-Jung, devoted herself to support my study and to raise two daughters. v

7 Finally, my special thanks go to my parents. They always had a great enthusiasm for higher education for their children. Moreover, my father taught me how to control myself, which is more valuable than knowledge itself. Without their sacri ce and devotion, I would not be what I am now. vi

8 VITA July 8, Born - Gueonchun, Republic of Korea B.A. Economics, Seoul National University, Republic of Korea Economist, The Bank of Korea, Republic of Korea M.A. Economics, The Ohio State University 24-present Graduate Teaching Associate, The Ohio State University FIELDS OF STUDY Major Field: Economics Studies in: Money and Macroeconomics Econometrics vii

9 TABLE OF CONTENTS Page Abstract Dedication Acknowledgments Vita List of Tables ii iv v vii x List of Figures xi Chapters: 1. INTRODUCTION REASSESSMENT OF THE NEW KEYNESIAN PHILLIPS CURVE: GROSS VS. VALUE-ADDED PRICE INFLATION Introduction Model Gross Price In ation Value-Added Price In ation Estimation of the Phillips Curve Concluding Remarks THE EMPIRICAL RELATIONSHIP BETWEEN THE MARKUP, MAR- GINAL COST AND INFLATION, AND ITS IMPLICATIONS FOR PRICE- SETTING MODELS viii

10 3.1 Introduction Empirical Impulse Responses of In ation Identi cation Strategy Evidence for Non-Stationary Markup Results of the VAR Implications for Price-Setting Models Model Economy Impulse Responses for the Model Economy Concluding Remarks CONCLUSIONS Appendices: A. DERIVATION OF (3.29) Bibliography ix

11 LIST OF TABLES Table Page 2.1 Correlation of Detrended Real Materials Price Related Series for Interpolation by Chow-Lin Procedure Estimation Results for Value-Added Price In ation with Di erent Speci cations Estimation Results for Gross Price In ation Estimation Results for Value-Added Price In ation with Real Price of Materials Estimation Results for Value-Added Price In ation without Real Price of Materials Results of Unit Root Test on Markup Results of Unit Root Test on Hours Parameterization x

12 LIST OF FIGURES Figure Page 2.1 Trend of Real Price of Materials in U.S. (Index, 199=1) Comparison of Labor Income Shares (Index, 1992=1, Log Scale) Comparison of Two Alternative Measures of Markup (Index, 1992=1, Log Scale) Trend of Per Capita Hours (Index, 1992=1, Log Scale) Trend of Hours Per Employee (Index, 1992=1, Log Scale) Comparison of Two Alternative Measures of Markup (VAR IRFs to Markup Shock) Impulse Responses to Markup Shock in VAR (Overhead Labor) Impulse Responses to Technology Shock in VAR (Overhead Labor) Impulse Responses to Demand Shock in VAR (Overhead Labor) Impulse Responses to Markup Shock in Calvo Model Impulse Responses to Technology Shock in Calvo Model Impulse Responses to Money Growth Shock in Calvo Model Impulse Responses to Markup Shock in Mankiw-Reis Model Impulse Responses to Technology Shock in Mankiw-Reis Model xi

13 3.14 Impulse Responses to Money Growth Shock in Mankiw-Reis Model Comparison of Actual In ation Response and In ation Predicted by Calvo Model xii

14 CHAPTER 1 INTRODUCTION Economists have long been interested in explaining how economic activities a ect in ation in the economy. The relationship between in ation and a variable that represents the strength/weakness of economic activities has been called the Phillips curve after the economist (A.W. Phillips) who rst documented a relationship between unemployment and the rate of change of nominal wages in the United Kingdom for the period The importance of the Phillips curve in the eld of macroeconomics can also be seen by Nobel laureate George Akerlof s remark: "Probably the single most important macroeconomic relationship is the Phillips curve." Although many researchers have devoted their time to nd theoretical foundations of this curve, none of the theories are fully satisfactory in explaining the actual in ation of the economy. Among them, however, the new Keynesian Phillips curve has received much attention and has been extensively used in analyzing policy issues. Derived from the optimizing behavior of individual rms, the new Keynesian Phillips curve shows that current in ation is determined by the expectations of future in ation and current economic activity. But some empirical studies show that the new Keynesian Phillips curve does not t U.S. data well when the output gap is used as a proxy for economic activity. Moreover, the model implies that in ation responds very 1

15 quickly to a monetary policy shock, which is inconsistent with the data. Empirical studies, for example Christiano et al. (25), nd that in ation displays a humpshaped response after an expansionary monetary policy shock. On these grounds, the new Keynesian Phillips curve has been highly criticized. There have been a number of attempts to resolve the problem of the new Keynesian Phillips curve. One attempt is made by Gali and Gertler (1999) who argue that the actual driving variable in the new Keynesian Phillips curve is real marginal cost, and that if the labor income share is used as a proxy for the real marginal cost, then the in ation model is well supported by the data. They assert that the empirical failure of the new Keynesian Phillips curve arises only when the output gap is used as a proxy for the real marginal cost. Another attempt is introduced by Mankiw and Reis (22) who propose a new in ation model called the sticky information Phillips curve. They argue that information about the state of the economy propagates slowly because there are costs associated with acquiring and processing information. Firms are modeled as updating their information, especially on their marginal cost, only infrequently. Thus when they make price decisions, a large portion of the decisions is still based on the past economic conditions, as a result of which in ation responds gradually to monetary policy shocks. This dissertation investigates the validity of the new Keynesian Phillips curve and the sticky information Phillips curve. The rst essay, in chapter 2, addresses issues associated with the new Keynesian Phillips curve. Unlike other approaches testing the new Keynesian in ation model, I pay attention to the distinction between the price of gross output (hereafter, gross price) and the price of value-added output (hereafter, 2

16 value-added price). In my interpretation, the price in the original pro t maximization problem of a representative rm corresponds to the gross price conceptually, in the sense that intermediate input costs are embedded in this price. Moreover, since the purchasers of the rm s products do not face the value-added price in the actual world and they pay the whole price including intermediate input costs, it is natural that an individual rm s demand schedule is expressed as a function of the gross price, not as a function of the value-added price. As a result, a standard new Keynesian Phillips curve can be interpreted as in ation behavior for the gross price. Accordingly, to test this in ation model, marginal cost measures should be constructed so as to explain the behavior of the gross price. Another way of testing the new Keynesian Phillips curve is to explicitly derive an in ation model for the value-added price and to use the GDP de ator as a measure of the value-added price. I apply in ation models for both the gross price and the value-added price to assess the new Keynesian Phillips curve. It turns out that, for both models, the data do not provide strong support for this forward-looking in ation behavior. However, in some subsamples, especially during high and volatile in ation periods, the evidence becomes stronger for the value-added price in ation model. Also it is shown that the e ects on in ation of real intermediate input prices and the backward-looking behavior of individual rms are substantial. The second essay, in chapter 3, starts with nding empirical responses of in ation to several structural shocks. For this purpose, a structural vector autoregression model is constructed to identify the e ects of shocks to the desired markup, technology and aggregate demand. The results of the model show that in ation responds immediately to shocks to the desired markup and technology whereas it displays a 3

17 hump-shaped response to a demand shock. Moreover, it is shown that the gradual response of in ation to a demand shock is caused by an inertial response of marginal cost, not by an inertial response of in ation to changes in marginal cost. The empirical ndings of this chapter have several implications for price-setting models. First, in light of the estimated immediate responses of in ation to the desired markup and technology shocks, the new Keynesian Phillips curve is quite consistent with the data while the sticky information Phillips curve implies inertial responses of in ation to these two shocks. Thus building a price-setting model that produces a hump-shaped response of in ation to any type of shock seems to be no longer necessary. Second, the new Keynesian Phillips curve need not be discarded simply because it fails to generate inertial in ation in response to a demand shock, especially a monetary policy shock. Given the actual response of marginal cost observed after a demand shock, it turns out that the new Keynesian Phillips curve can produce an inertial response of in ation. Then its failure to generate humpshaped in ation in response to a demand shock appears to be associated with poorly modeling the movement of production costs rather than the price-setting behavior itself. Therefore, the complete explanation of the inertia in in ation that occurs after a demand shock would require a thorough overhaul of the elements that a ect marginal cost. 4

18 CHAPTER 2 REASSESSMENT OF THE NEW KEYNESIAN PHILLIPS CURVE: GROSS VS. VALUE-ADDED PRICE INFLATION 2.1 Introduction The determinants of in ation dynamics have long been a subject of macroeconomics. Although much e ort has been devoted to this issue, the dynamics of in ation are not fully understood. Recently, much attention has been focused on the new Keynesian Phillips curve, which builds on the work of Calvo (1983). This in ation model is successful in some sense since it explains why future in ation expectations determine current in ation. This is due to the optimizing behavior of individual rms. According to the standard new Keynesian Phillips curve, current in ation is determined by expectations of future in ation and the current output gap or alternatively current real marginal cost. There has been much debate on the validity of this in ation equation. Gali and Gertler (1999) show that, when current in ation is regressed on future in ation and the output gap, the sign of the output gap coe cient is negative, which is contrary to theoretical predictions. However, they argue that this empirical failure arises not from the new Keynesian Phillips curve itself but from the inappropriateness of the output gap as a proxy for real marginal cost. They instead 5

19 show that real unit labor cost (the labor income share) is a better measure of real marginal cost, and provide evidence that the new Keynesian Phillips curve ts well with U.S. data. Woodford (21) argues that deterministically detrended real GDP is a poor measure of output gap. He points out that detrended real GDP does not track the di erence between actual output and potential output, i.e., the equilibrium level of output when prices are fully exible. Noting that the actual driving variable in the new Keynesian Phillips curve is real marginal cost, he shows that this in ation equation works well when this measure of real marginal cost is used instead of the output gap. Sbordone (22) also nds evidence that supports the new Keynesian Phillips curve, based upon the prediction results of this forward-looking in ation model. Rudd and Whelan (22) test whether the labor income share is a good measure of real marginal cost. They show that the new Keynesian Phillips curve with labor income share as a proxy for real marginal cost does not t well with U.S. in ation. Speci cally, they nd no evidence that the discounted sum of current and expected future labor income share explains the actual movement of in ation, and conclude that the labor income share does not seem to drive in ation. In this connection, Rotemberg and Woodford (1999) illustrate several reasons why labor income share might be an inappropriate measure of real marginal cost. They point out that the existence of overhead labor, overtime premium and adjustment cost for labor can create a discrepancy between real marginal cost and the labor income share. In this respect, measuring marginal cost is a crucial element in assessing di erent views on in ation dynamics. Unfortunately, marginal cost is not observable. Thus, measuring marginal cost usually relies on theoretical assumptions on the structure of 6

20 the economy. For example, Gali and Gertler (1999) assume that rms take input prices including wages and the rental price of capital as given, and that the production function is Cobb-Douglas. On the other hand, di erent production functions are sometimes used. Balakrishnan and Lopez-Salido (22) attempt to explain the behavior of in ation in an open economy context. Taking into account the fact that the United Kingdom imports a signi cant amount of materials as production inputs, they employ a CES production function to incorporate imported materials. However, the more crucial element, which I address in this chapter, is the conceptual correspondence of marginal cost and the price level in the model. Since almost all products require both intermediate inputs and primary inputs such as labor and capital, it is essential to incorporate the movement of intermediate input costs into marginal cost measures. Traditionally, the treatment of intermediate inputs has not been explicit in economic analyses, the practice of which can be justi ed under the assumption of perfect competition. Under perfect competition, value-added production functions exist and the pro t maximization problem of a representative rm can be stated in terms of the price and quantity of value-added output and the cost for primary inputs. As is noted in Rotemberg and Woodford (1993), however, under an imperfect competition environment in which individual rms set their own prices, the traditional practice can no longer be justi ed. In this case, attention should be shifted to gross output production functions and thus the cost for intermediate inputs should also be included in total production cost. An issue associated with Gali and Gertler s (1999) approach is to nd the microfoundation of using GDP de ator as a general price measure, which is the price of value-added output (hereafter, value-added price). Since, for the economy as a 7

21 whole, value-added output equals the output of nal products such as consumption and investment goods, the value-added price of the whole economy can be interpreted as the price of nal products. Moreover, due to the fact that producing nal products requires both intermediate inputs and primary inputs, the price of nal products re ects both intermediate and primary input costs. Thus if one wants to employ the GDP de ator as a price level measure, one should construct production cost measures that capture the cost variation of intermediate inputs and primary inputs in the sectors that produce nal products. This approach, however, is not practical because it is hard to distinguish between the sectors that produce nal products and the sectors that produce intermediate inputs. Therefore, if one wants to use the GDP de ator to study in ation behavior, a di erent approach is needed. The objective of this chapter is to reexamine the validity of the new Keynesian Phillips curve. Unlike other approaches testing the in ation equation, I pay attention to the distinction between the price of gross output (hereafter, gross price) and the value-added price. In my interpretation, the price in the original pro t maximization problem of a representative rm corresponds to the gross price conceptually, in the sense that intermediate input costs are embedded in this price. Moreover, since the purchasers of products do not face the value-added price in the actual world and they pay the whole price including intermediate input costs, it is natural that an individual rm s demand schedule is expressed as a function of the gross price, not as a function of the value-added price. As a result, the standard new Keynesian Phillips curve can be interpreted as in ation behavior for the gross price. Accordingly, to test this in ation equation, marginal cost measures should be constructed so as to explain the behavior of the gross price. Another way of testing the new Keynesian 8

22 Phillips curve is to explicitly derive a value-added price in ation equation and to use the GDP de ator as a value-added price measure. In this chapter, I apply in ation models for both the gross price and the value-added price to assess the new Keynesian Phillips curve. It turns out that, for both models, the data do not provide strong support for this forward-looking in ation behavior. However, in some subsamples, especially during high and volatile in ation periods, the evidence becomes stronger for the value-added price in ation model. The organization of this chapter is as follows. First, I develop models for gross price and value-added price in ation in section 2.2. Keynesian Phillips curve using both in ation models. In section 2.3, I test the new Finally, some conclusions are drawn in section Model Gross Price In ation The economy consists of a continuum of households and rms indexed by i on [; 1] and the government. Each rm produces a di erentiated product which can be used either as an intermediate input or for nal demand such as consumption and investment. As in Basu (1995), products are distinguished by use, not by type of products. A representative household maximizes lifetime expected utility subject to standard budget constraints: Max: E 1P t= 1 t 1 C t(j) 1 H t (j) (2.1) where is a discount factor; C t (j) and H t (j) denote household j s consumption demand and labor supply at time t, respectively. Furthermore, C t (j) is a CES 9

23 h R "=(" 1) 1 aggregator such that C t (j) = C t(i; j) dii (" 1)=" in which " is the elasticity of substitution between di erentiated products and C t (i; j) is household j s consumption demand for the i-th product. From the rst order conditions and by aggregating across all households, we obtain aggregate consumption demand for the i-th product: CD t (i) = Z 1 " Pt (i) C t (i; j)dj = C t (2.2) where C t = R 1 C t(j)dj is the aggregate consumption demand of the whole economy, h R 1=(1 ") 1 P t (i) is the price of the i-th product and P t = P t(i) dii 1 " is the corresponding aggregate price index. In order to derive a nal demand function for the i-th product, we can follow the approach of Woodford (23, p.354) assuming that all economic agents including the government minimize total expenditures given the aggregate demand for nal P t products. Then we have: " Pt (i) F D t (i) = F D t (2.3) where F D t (i) denotes the nal demand for the i-th product and F D t is the aggregate nal demand of the whole economy. Now we can extend this result to gross output demand of the i-th product if we assume that a representative rm minimizes the total cost of intermediate inputs (hereafter, materials) given the total quantity of materials demand: P t Min: Z 1 Z 1 " P t (i)m t (i; j)di s:t: M t (j) = M t (i; j) " 1 " di " 1 (2.4) where M t (i; j) denotes rm j s materials demand for the i-th product, and M t (j) is the total quantity of materials demand of rm j. 1

24 From the rst order conditions, we have " Pt (i) M t (i; j) = M t (j): (2.5) P t By aggregating across all rms, we obtain aggregate materials demand for the i-th product: MD t (i) = Z 1 " Pt (i) M t (i; j)dj = M t (2.6) where M t = R 1 M t(j)dj is the aggregate materials demand of the whole economy. Therefore, gross output demand for the i-th product is P t " Pt (i) Q t (i) = MD t (i) + F D t (i) = Q t (2.7) where Q t = M t + F D t is the gross output of the whole economy. P t A representative rm is assumed to maximize pro ts under the Calvo-type environment in which the rm can only adjust its price with a certain probability: Max: 1P E t Pt (j)q t (j) t= t M t (j) W t L t (j) Rt k K t (j) P m P t (2.8) where P m t ; W t ; R k t are the price of materials, wage rate and the user cost (or rental price) of capital, respectively; L t (j) and K t (j) are labor and capital demand of rm j, respectively. This rm faces a gross output demand function of the form (2.7) for the j-th product and the following xed proportions production technology that has been used by Rotemberg and Woodford (1993), Basu (1996), and Conley and Dupor (23). Q t (j) = f(m t (j); L t (j); K t (j)) (2.9) Mt (j) Mt (j) = min ; g(l t (j); K t (j)) = min ; A t L t (j) K t (j) 1 t t 11

25 where A t is the productivity associated with labor and capital inputs and t is the quantity of materials needed to produce one unit of gross output. Moreover, it is assumed that all rms have the same production technology. In this setting, we can obtain a standard new Keynesian Phillips curve of the following form: ^ t = E t^ t+1 + cmc t (2.1) where ^ implies a percentage deviation from the steady state value, t is de ned as t P t =P t 1, and mc t denotes the average real marginal cost of the economy at time t. Here the parameter is (1 )(1 )= where is a discount factor and is the probability of a representative rm s not adjusting its price. Now it is obvious that this in ation equation describes the behavior of gross price, and that the marginal cost re ects costs for both materials and primary inputs. With the production function stated above, the real marginal cost is mc t = P t m P t + 1 W t L t (2.11) t P t Q t where L t = R 1 L(j)dj is aggregate labor.1 The implication of this real marginal cost measure is that the movement of production cost is not fully captured by labor cost in the case that materials are not substitutable with primary inputs. Therefore, we 1 To derive this real marginal cost measure on the aggregate level, we need to de ne another quantity index, Q t = R 1 Q(j)dj as is applied by Yun (1996). Then rm j s real marginal cost is: mc t (j) = P t m P t + 1 W t L t (j) t P t Q t (j) = P t m P t + 1 W t L t t P t Q t = P t m P t + 1 W t L t Q t t P t Q t Q for all j: t These two kinds of quantity indexes have the same value at the steady state and deviations form the steady state value of two quantity indexes are approximately the same. Therefore, we can measure the average real marginal cost of the economy by (2.11). Likewise, t (= M t (j)=q t (j)) can be measured by the aggregate data, M t =Q t : 12

26 need an additional term of the real price (or relative price) of materials to re ect changes in materials cost. On the aggregate level, however, materials price (Pt m ) turns out to be equal to aggregate price (P t ) when rms use materials that are produced only in the domestic economy. There should be no uctuations in the real materials price in this case. Then, the real marginal cost measure in (2.11) provides little additional information on variations in production cost. But as is seen in gure 2.1, the real materials price has been changing all the time, and sometimes changes in the real materials price have had an enormous in uence on the economy, especially during the two oil shocks in the 197s. In order to explain uctuations in real materials price, I include imported materials in the total quantity of materials. 2 In this open economy context, (2.3) can easily be interpreted to include exports. We assume that there is a continuum of imported materials indexed by i on [; 1]. Then (2.4) can be modi ed to Min: Z 1 P t (i)m d t (i; j)di + Z 1 s:t: Mt d (j) = Z 1 M f t (j) = Z 1 " Mt d (i; j) " 1 " di P f t (i)m f t (i; j)di (2.12) " 1 " 1 " M f t (i; j) " 1 " di where P f t (i) is the price of the i-th materials imported from foreign countries; M d t (i; j) and M f t (i; j) are rm j s demand for the i-th domestically produced materials and 2 For simplicity, it is assumed that only materials are imported from abroad. In reality, consumption and investment goods can also be imported. Even this case, however, can be modeled in the same way to show the same conclusions. ; 13

27 imported materials, respectively; and M d t (j) and M f t (j) are rm j s total quantity demanded of domestically produced materials and imported materials. 3 Then the rst order conditions give M d t (i; j) = M f t (i; j) = " Pt (i) Mt d (j) (2.13) P t! " P f t (i) M f P f t (j) t h R 1=(1 ") where P f 1 t = P f t (i) dii 1 " is the aggregate price index of imported materials. Again by aggregating across all rms, we have demand functions of the domestically produced materials and the imported materials for the i-th product: MD d t (i) = MD f t (i) = Z 1 Z 1 " Mt d Pt (i) (i; j)dj = Mt d (2.14) P t! M f t (i; j)dj = P " f M f t t (i) P f t 3 In this case, I implicitly assume that the production function of rm j is of the form: " # Mt d (j) M f t (j) Q t (j) = min ; ; A t L t (j) K t (j) 1 d t f t where d t and f t are the quantity of domestically produced materials and imported materials needed to produce one unit of gross output, repectively. This assumption ensures the additivity of materials (that is, M t (j) = M d t (j) + M f t (j)) and the national income identity, which will be discussed later, if we de ne the price index for materials by Pt m = d t P d t + f t P f t +f t d t +f t. Alternatively, we can assume t that domestically produced materials are substitutable with imported materials. In the latter case, we assume the same production function as (2.9), but need to modify the cost minimization problem (2.12) as the following: Min: Z 1 P t (i)m d t (i; j)di + Z 1 P f t (i)m f t (i; j)di Z 1 Z 1 " s:t: M t (j) = k Mt d (i; j) " 1 " di + M f t (i; j) " 1 " 1 i " di = k hmt d (j) " 1 " + M f t (j) " 1 " " 1 " : In this latter case, the additivity of materials will hold only at the steady state. 14

28 where M d t = R 1 M d t (j)dj and M f t = R 1 M f t (j)dj are the aggregate demand of the whole economy for domestically produced materials and imported materials, respectively. Now (2.7) holds with a slight modi cation: " Q t (i) = MDt d Pt (i) (i) + F D t (i) = Q t (2.15) where the gross output of the whole economy is now de ned as Q t = M d t + F D t. Therefore, even in the open economy context, we have (2.1) and (2.11) with an P t interpretation that t = d t + f t and P m t = ( d t =( d t + f t ))P t + ( f t =( d t + f t ))P f t Value-Added Price In ation When researchers test the new Keynesian Phillips curve, they usually use the GDP de ator as a general measure of price level. In this case, they are implicitly assuming the following in ation equation for the value-added price: ^ v t = E t^ v t+1 + cmc v t (2.16) where v t denotes the in ation rate of value-added price (P v t =P v t 1), and mc v t is the real marginal cost of producing one unit of value-added output at time t. However, it is unclear whether we can have such a value-added price in ation equation on theoretical grounds. If we are able to derive a new value-added price in ation equation that may or may not be of the form (2.16), then there will be two ways of testing the new Keynesian Phillips curve. Either we can test the gross price in ation equation, or we can test a value-added price in ation equation. 15

29 To nd a value-added price in ation equation, we start from the following two identities: P t Q t = Pt m M t + Pt v Y t (2.17) Q t = M t + Y t where P v t is aggregate value-added price and Y t denotes the value-added output of the whole economy. The rst identity states that nominal gross output (total revenue) is the sum of nominal materials cost and nominal value-added. The second identity states that this relationship also holds in real terms. 4 Thus gross price is expressed as the weighted average of materials price and value-added price: Y t P t = Pt m M t + Pt v : (2.18) Q t Q t In general, t in (2.9) may be time-varying due to technological changes over time. For the derivation of value-added price in ation equation, I assume that t is constant over time (i.e., t = ). Then we have the relationship between gross price in ation and value-added price in ation as follows: 5 t = P t P t 1 = (1 )P v t (1 )P v t 4 This can be shown by the following: + P m t 1 + P m t 1 = (1 )v t + m t R t 1 (1 ) + R t 1 Q t = M d t + F D t = M d t + M f t + F D t M f t By the additivity of materials, M d t + M f t = M t. According to the national income identity, valueadded output = consumption + investment + export - import. Therefore, F D t M f t = Y t. 5 Since M t (j) = Q t (j); M t = R 1 M t(j)dj = R 1 Q t(j)dj = Q t : Then M t Q t = M t Q t Q = Q t ; t Q t Q t Y t Q t = 1 M t Q t = 1 Q t Q t : At the steady state, the two quantity indexes of gross output have the same value and deviations from the steady state values are approximately the same. Therefore, M t =Q t and Y t =Q t are approximately equal to and 1, respectively. 16

30 where m t is the in ation rate of materials price (Pt m =Pt m 1), and R t 1 is the real price of materials at time t 1 (Pt m 1=Pt v 1). Log-linearization of the above equation leads to an equation that shows the relationship between gross price in ation and value-added price in ation, all expressed as deviations from the steady state values: (1 ) v ^ t = (1 ) + R ^ v t + R m (1 ) + R R + m (1 ) + R 1 ^R t 1 ^ m t where an upper bar denotes the steady state value of each variable. If we assume that the real price of materials is stationary, then the steady state values for t ; v t and m t will be the same. Moreover, since the real materials price is the ratio of two price indexes, we can change the base year to normalize the steady state value of real materials price to one ( R = 1). The above simpli es to ^ t = (1 )^ v t + ^ m t : (2.19) Therefore, just as the gross price is expressed as the weighted average of value-added price and materials price, this relation also holds for percentage deviations from the steady state. Now let us turn to the relationship between the real marginal cost of producing one unit of gross output (mc t ) and the real marginal cost of producing one unit of value-added output (mc v t ). From (2.11) and after modi cations, mc t = P t m M t + 1 W t L t = P t Q t P t Q t 1 P m t P v t + 1 W t L t Pt v Y t Pt m Pt v Note that xed proportions technology entails a value-added output production function of Cobb-Douglas form, that is, Y t = Z t L t Kt 1 where Z t is de ned by (1 )A t. 17 :

31 In this case, it is shown in Gali and Gertler (1999) that the real marginal cost of producing one unit of value-added output (mc v t ) is proportional to labor income share (mc v t = (1=)(W t L t =P v t Y t )). Therefore, mc t = 1 R t + mc v t : (2.2) 1 R t + 1 Finally, by log-linearization around the steady state, cmc t = (1 ) mcv 1 mc cmcv t + mc 1 ^R t : (2.21) where mc v and mc are the steady state values of mc v t and mc t, respectively. It is shown that the real marginal cost of producing one unit of gross output is determined not only by the real marginal cost of producing one unit of value-added output, which in turn is a ected by real wages and labor productivity, but also by real materials price. Under perfect competition, prices are equal to nominal marginal cost and thus the second term in (2.21) vanishes. In this case, the real marginal cost of gross output is fully explained by the labor income share. Under imperfect competition, however, this is no longer true. A marginal cost measure that does not re ect the movement of materials price does not provide accurate information on changes in production cost. Then, by substituting (2.19) and (2.21) into (2.1) and from (2.2), we have the following equation for value-added price in ation: ^ v t = E t^ v t E t^ m t (1 ) cmcv t + 1 ( 1) ^R t 1 ^m t : (2.22) where ( 1=mc) is the steady state value of gross markup ratio ( = "=(" 1) in this model). Since ^ v t = [1=(1 )] ^ t [=(1 )] ^ m t from (2.19), it is obvious that gross 18

32 price in ation positively a ects value-added price in ation. But the interpretation about the second term needs some caution. If the materials price rises, then this will be embedded in gross price movement. However, if the gross price does not change in response to an increase in materials price, then this will have a negative e ect on value-added price. Thus the second term re ects the e ect of materials price change on value-added in ation when gross price does not change in response to materials price movement. In this regard, (2.22) shows that value-added price in ation is determined not only by expectations on future value-added price in ation (E t^ v t+1) and the real marginal cost of value-added output ( cmc v t ), but also by expectations on future materials price movement (E t^ m t+1) and the current real materials price ( ^R t ). The last term in equation (2.22) re ects the negative impact of materials price change when gross price is not adjusted in response to materials price movement. Alternatively, from the de nition of the real price of materials, we can obtain another expression that depicts the behavior of value-added price in ation. That is, since R t Pt m =Pt v ; we have ^ m t = ^ v t + ^R t ^Rt 1 = ^ v t + ^R t : The movement of materials price can be replaced by the change in the real price of materials. Thus (2.22) implies ^ v t = E t^ v t+1 + (1 ) cmc v t + ( 1) ^R t + E t ^R t+1 ^R t : (2.23) This expression shows that, compared to (2.16), real materials price ( ^R t ) and changes in real materials price (E t ^R t+1 ; ^R t ) play an important role in explaining the behavior of value-added price in ation. Real materials price ( ^R t ) a ects valueadded price in ation through the e ect on the real marginal cost of gross output. 19

33 Expectations on future change in real materials price (E t ^R t+1 ) re ect the future expectation e ect of materials price movement (E t^ m t+1), and the current change in real materials price ( ^R t ) shows the negative e ect of materials price change when gross price is not adjusted in response to materials price movement. In a special case when real materials price is constant, equation (2.23) reduces to ^ v t = E t^ v t+1 + (1 ) cmc v t ; (2.24) which has the same form as the equation (2.16) with a slight change in the coe cient on the real marginal cost of value-added output. 6 Therefore, it is clear that the behavior of value-added price in ation cannot be fully explained by the movement of labor income share in an economy where there are uctuations in the real price of materials. 2.3 Estimation of the Phillips Curve As is noted by Gali and Gertler (1999), the purely forward-looking in ation model (baseline model) is not appropriate for explaining in ation inertia, which is observed in empirical studies. Taking into account this point, they introduce backward-looking agents who set their price according to the average behavior of the economy in the previous period, and employ adaptive expectations to make a correction for in ation. Assuming that the portion of this type of backward-looking agents is!, they derive the following hybrid model that can nest both forward-looking and backward-looking expectations: ^ t = 1 E t^ t+1 + 2^ t 1 + cmc t (2.25) 6 Since mcv mc = 1 (1 ) from (2.2), (1 ) should be positive. 1 2

34 where 1 = =[ +!(1 (1 ))]; 2 =!=[ +!(1 (1 ))] and = (1!)(1 )(1 )=[ +!(1 (1 ))]. Their estimation results show that this hybrid in ation model depicts the actual in ation behavior fairly well. In this respect, evaluating the validity of the new Keynesian Phillips curve should be based on testing both the baseline and the hybrid model. In view of the argument of the previous section, this hybrid in ation model is interpreted as describing the behavior of the gross price, not the value-added price. This being the case, we should test equation (2.25) by using the gross price in ation rate and a real marginal cost measure that is conformable to the gross output concept. The alternative method is to derive a hybrid model of value-added price in ation. Applying similar procedures from the previous section, we obtain the following in ation equation for the valueadded price that combines both forward-looking and backward-looking expectations: b v t = 1 E t b v t b v t 1 + (1 ) cmc v t + ( 1) R b t (2.26) + 1 E t ^R t+1 ^R t + 2 ^R t 1 : Compared to (2.23), we additionally have the lag terms of value-added price in ation (b v t 1) and a change in real materials price ( ^R t 1 ), both of which re ect the backward-looking expectations e ect on current in ation. Tests of the new Keynesian Phillips curve are performed using both in ation equations for gross price and value-added price. Moreover, for each in ation equation, both the baseline and the hybrid model are tested. To estimate the new Keynesian Phillips curve, I apply the generalized method of moments (GMM). 7 These in ation models can be tested either by estimating slope coe cients (for example, 1, 2 and 7 Before applying GMM, in ation equations expressed in terms of deviations from the steady state value are converted to in ation equations expressed in terms of percentage changes from the 21

35 in (2.25)) or by directly estimating the structural parameters (for example,,,! in (2.25)). For gross price in ation models (2.1) and (2.25), the structural parameters can be exactly identi ed from the estimates of slope coe cients. In this case, the two methods should yield exactly the same result. However, estimating the structural parameters involves nonlinear optimization procedures, which sometimes failed to achieve convergence. Therefore, gross price in ation models are tested by estimating slope coe cients. For value-added price in ation models (2.23) and (2.26), estimating the structural parameters directly is equivalent to imposing restrictions on the slope coe cients of equations in footnote 7 (for example, 1 5 = 3 in the case of baseline model). If the restrictions are valid, this method yields more e cient estimates. The restrictions are tested by applying the GMM equivalent test of likelihood ratio type (distance di erence test). It turns out that test statistics do not reject the restrictions. 8 Therefore, value-added price in ation models are tested by directly estimating the structural parameters. previous period. For value-added price in ation equations, coe cients on ^R t+1 ; ^R t and ^R t 1 for the baseline models, and coe cients on ^R t+1 ; ^R t ; ^R t 1 and ^R t 2 for the hybrid model are collected together to yield: p v t = 1 E t p v t cmc v t + 3 E t b Rt b Rt + 5 b Rt 1 p v t = 1 E t p v t p v t cmc v t + 4 E t b Rt b Rt + 6 b Rt b Rt 2 where lower case letter p v t denotes the logarithm of value-added price level (P v t ), and each coe cient is as follows: 1 = ; 2 = (1 ); 3 = ; 4 = [1 + ( 1)]; 5 = ; 1 = 1 ; 2 = 2 ; 3 = (1 ); 4 = 1 ; 5 = [1 + 1 ( 1)]; 6 = (1 + 2 ); 7 = 2 : In this case, predicted signs for the coe cients 4, 5 and 7 are negative while the signs for the other coe cients are expected to be positive. Unless the markup ratio () is implausibly high, expecting negative signs for 4 and 5 seems to be reasonable. 8 For the baseline model, the number of restrictions is one, and the chi-square statistic is.421. For the hybrid model, the number of restrictions is two, and the chi-square statistic is

36 The problem of estimating (2.23) and (2.26) without terms related to the real materials price is that the orthogonality conditions are violated. The orthogonality conditions from (2.23) and (2.26) are based on the one-period ahead forecast error, which should be uncorrelated with variables in the current information set (instrument variables). However, if we omit terms related to the real materials price in (2.23) and (2.26), then the error term includes both one-period ahead forecast error and terms related to the real materials price. In this case, the error term is no longer orthogonal to the variables in the current information set since these instrument variables - such as the in ation rate, the detrended labor income share and the output gap - will be correlated with the movements of the real materials price. In fact, as table 2.1 shows, while correlation between the detrended real materials price and the leads and lags of the detrended labor income share is negligible, correlation between the detrended real materials price and the leads and lags of the in ation rate (and also of the output gap) is strong. This suggests that estimating the new Keynesian Phillips curve without the real materials price may lead to suspicious results. For the estimation of value-added price in ation equation, the U.S. GDP de ator is value-added price index, and labor income share is the real marginal cost of valueadded output (mc v t ). The materials price index is constructed by averaging two components of the producer price index that are compiled according to the stage of processing. One component is an index for crude materials for further processing and the other component is an index for intermediate materials, supplies and components. I assign.15 to crude materials and.85 to intermediate materials as weights for both indexes. These weights are computed from the 1997 benchmark input-output table 23

37 of the U.S. economy. 9 Then the real materials price (R t ) is computed by dividing this materials price index by the GDP de ator. The instrument set includes four lags of the value-added price in ation rate, the detrended labor income share, the detrended real materials price and the output gap. The output gap is measured with an HP- ltered real GDP and all the other detrended variables are computed with HP- ltering. The estimation of the gross price in ation equation is con ned to the manufacturing sector as a whole. The Bureau of Economic Analysis (BEA) constructs annual price and quantity indexes for gross output, intermediate inputs and value-added. However, data for the whole economy are available only after Data for the manufacturing sector are available from 1977 to 22. In this case, the real marginal cost measure in (2.11) should be computed to capture the cost movement of the manufacturing sector. Thus all of the data that I employ here are statistics for the manufacturing sector. The price index for gross output is used as gross price (P t ), the price index for intermediate inputs as materials price (Pt m ), the quantity index for gross output as gross output (Q t ), the compensation of employees as labor cost (W t L t ). To compute t, the quantity index for intermediate inputs is divided by the quantity index for gross output. I use.78 as the value for technology parameter. The calibration is based on the remark in Basu (1996) that the average pro t rate in U.S. manufacturing sector is less than four percent. Assuming that the average pro t rate is four percent, this implies that the average markup ratio () is equal to 1.4, which in turn gives the number for. In order to make a meaningful interpretation 9 The weight for crude materials re ects the purchase of agricultural and mining products from all industries, and the weight for intermediate materials includes the purchase of manufacturing products and utilities from all industries. 24

38 on a quarterly frequency, I interpolate the annual data with the method proposed by Chow and Lin (1971). This Chow-Lin procedure estimates quarterly data for available annual time series by regression on related series. Therefore, the accuracy of this interpolation method depends on how closely the related series are related to the original series both in concept and in actual movement. The data that I use as the related series are summarized in table 2.2. The instrument set includes four lags of the gross price in ation rate, detrended real marginal cost and the output gap. Since the orthogonality conditions are based on one-period ahead forecast error, the GMM disturbance term (the product of forecast error and instrument vector) does not have serial correlation. However, we cannot exclude the possibility of heteroskedasticity of the GMM disturbance term. To consider this e ect, White s covariance matrix is used for the estimation of both in ation models. Estimation results for value-added price in ation are provided in table 2.3. The sample period for this estimation is from the rst quarter of 196 to the fourth quarter of 23. In this table, estimates for in ation models without the real price of materials are also provided in order to make comparisons across di erent models. Models 1 and 2 are in ation models without the real price of materials, the rst one being a purely forward-looking model (baseline model) and the second one a combination of forward and backward-looking behavior (hybrid model). Models 3 and 4 are in ation models with the real price of materials, again the former being the baseline model and the latter the hybrid model. Estimation results for models 1 and 2 are similar to those in Gali and Gertler (1999). The coe cient on the real marginal cost is highly signi cant (.51 with standard error.18 in model 1 and.41 with standard error.15 in model 2). However, if we use in ation models with the real price of materials, the 25