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Essays on output and real exchange rate dynamics Khan, Hashmat Ullah 1999

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E S S A Y S O N O U T P U T A N D R E A L E X C H A N G E R A T E D Y N A M I C S by HASHMAT U L L A H K H A N B.A. (Honours), University of Delhi, 1989 M.A., University of Delhi, 1991 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF T H E REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in T H E FACULTY OF GRADUATE STUDIES Department of Economics We accept this thesis as conforming to the required standard TH# UNIVERSITY OF BRITISH COLUMBIA September 1999 ©Hashmat Ullah Khan, 1999 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the library shall make it freely available for reference and study. I further agree that permission for extensive copying of the thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It, is understood that copying or publication of the thesis for financial gain shall not be allowed without my written permission. Department of Economics The University of British Columbia # 997-1873 East Mall Vancouver, B.C., Canada V6T 1Z1 Date: Abstract There are two key observations in international macroeconomics which pertain to output and real exchange rate dynamics. First, fluctuations in national output around its long-run growth path are very persistent. Second, fluctuations in real exchange rates are very persistent. The sticky price framework offers an explanation for both phenomena. The first and second essay of this thesis take an empirical approach to test the predictions of this framework. In the first essay I test the prediction of the sticky price model for output dynamics using annual IFS data on 51 countries over the period 1950 -1996. The model predicts that price stickiness should be less important in high inflation countries and therefore output fluctuations less persistent. I find that, this inverse relationship is statistically insignificant in the international data. A similar result holds for O E C D countries. In the empirical implementation I explicitly control for the within-country time variation in inflation by first characterizing the inflationary environment using the long-run movements in inflation (trend inflation), and secondly, by excluding episodes of hyperinflation. The analysis shows that when the within-country time variation in inflation is ignored, there is support for the prediction. For instance, the inverse relationship between persistence in deviations of output from its long-run growth path and average inflation is statistically significant in the full sample. However, the exclusion of a few episodes of hyperinflation renders this relationship statistically insignificant. In the second essay I investigate the prediction of the sticky price model for real ex-change rate dynamics using annual IFS data on 49 countries over the period 1972-1996. The model predicts that deviations of real exchange rates from purchasing power parity should be less persistent, in high inflation countries. The empirical analysis reveals that the support for such an inverse relationship is extremely fragile. In particular, eliminating episodes of hyperinflation renders this relationship statistically insignificant. The lack of evidence in favour of the two predictions of the sticky price model is prob-lematic since this model is extensively used as a microfoundation for understanding output and real exchange rate fluctuations. In the third essay I take a structural approach to qualitatively explore the role of slow diffusion of new products in propagating the effect of technology shocks on output. I present a multi-sector dynamic general equilibrium model in which the creation of new products requires real resources. These products are beneficial for the economy but only upon complete diffusion. However, this diffusion is not instantaneous. I find that rela-tive to a model in which there is instantaneous diffusion of new products, the qualitative output dynamics are similar to what is observed in the U.S. data. This warrants further quantitative investigation. n Contents Abstract ii Acknowledgement ix Contents iii List of Tables v List of Figures v i i i Chapter 1 Introduction 1 1.1 The Contribution of This Thesis 2 Chapter 2 Price Stickiness, Inflation, and Output Dynamics: A Cross-country Analysis 7 2.2 Theoretical Framework 10 2.3 Empirical Implementation 13 ' 2.3.1 AR(1) Output Dynamics 16 2.3.2 Data 17 2.4 Results 18 2.4.1 Excluding Episodes of Hyperinflation 22 2.4.2 AR(2) Output Dynamics 28 2.5 Output Dynamics: OECD and NON-OECD Countries 31 2.6 The Two Stage Estimation 37 2.6.1 AR(1) Specification 37 2.6.2 The Inverted-U Relationship 39 2.6.3 Episodes of Hyperinflation 39 2.6.4 Alternative Measures of Persistence 40 2.6.5 Other Country-Specific Characteristics 45 2.7 Concluding Remarks 46 Chapter 3 Price Stickiness, Inflation, and Real Exchange Rate Dynam-ics: A Cross-Country Analysis 49 3.2 Theoretical Framework 52 3.3 Empirical Implementation 53 3.3.1 Data 55 3.4 Results 56 3.4.1 Episodes of Hyperinflation 57 3.4.2 OECD and Non-OECD Countries 62 iii 3.4.3 Two-Stage Estimation 65 3.4.4 Volatility Of Real Exchange Rates and Average Inflation 65 3.5 Discussion 67 3.5.1 Market Incompleteness 67 3.5.2 Distortionary Taxation 67 3.5.3 Strategic Price Competition 68 3.5.4 Non-monetary shocks 68 3.6 Conclusion 68 Data Summary 69 Chapter 4 Product Diffusion, Increasing Returns to Specialization, and the Propagation of Shocks 71 4.2 Model 73 4.2.1 Final Good Sector 74 4.2.2 Intermediate Goods Sector 75 4.2.3 Innovation Sector 76 4.2.4 Capital Accumulation 77 4.2.5 Feasibility Condition 78 4.2.6 Representative Consumer-Household 78 4.3 Market Clearing and Symmetric Equilibrium Conditions 79 4.4 Equilibrium Characterization 82 4.5 Calibration and Results 83 4.5.1 Economy-wide shock: U>Z=U>Q= 0.95 86 4.6 Conclusion 88 Appendix 95 Chapter 5 Conclusion 101 Bibliography 103 i v List of Tables 2.1 Persistence and Trend Inflation: QTD 19 2.2 Persistence and Trend Inflation: HP 19 2.3 Persistence and Average Inflation: QTD 19 2.4 Persistence and Average Inflation: HP 20 2.5 Persistence and Trend Inflation: QTD, with xt 20 2.6 Persistence and Trend Inflation: HP, with xt 21 2.7 Persistence and Trend Inflation: QTD, with xuN 21 2.8 Persistence and Trend Inflation: HP, with x^N 21 2.9 Persistence and Average Inflation: QTD, with xt 22 2.10 Persistence and Average Inflation: HP,with xt 22 2.11 Episodes of Hyperinflation 23 2.12 Persistence and Average Inflation: QTD, Excl. Episodes of Hyperinflation . 27 2.13 Persistence and Average Inflation: QTD,with xt, Excl. Episodes of Hyper-inflation 27 2.14 Persistence and Average Inflation: HP, Excl. Episodes of Hyperinflation . . 27 2.15 Persistence and Average Inflation: HP,with xt, Excl. Episodes of Hyperin-flation 28 2.16 Persistence and Trend Inflation: AR(2), QTD 29 2.17 Persistence and Trend Inflation: AR(2), HP 29 2.18 Persistence and Average Inflation: AR(2), QTD 30 2.19 Persistence and Average Inflation: AR(2), HP 30 2.20 Persistence and Average Inflation: AR(2), QTD, Excl. Episodes of Hyper-inflation 31 2.21 Persistence and Average Inflation: AR(2), HP, Episodes of Hyperinflation . 31 2.22 Persistence and Trend Inflation: HP, with xt, OECD Countries, N=22 . . . 32 2.23 Persistence and Trend Inflation: QTD, with xt, OECD Countries, N=22 . . 32 2.24 Persistence and Average Inflation: HP, with xt, OECD Countries, N=22 . . 32 2.25 Persistence and Average Inflation: QTD, with xt, OECD Countries, N=22 . 33 2.26 Persistence and Trend Inflation: AR(2), HP, with xu OECD Countries, N=22 33 2.27 Persistence and Trend Inflation: AR(2), QTD, with xt, OECD Countries, N=22 33 V; 2.28 Persistence and Average Inflation: QTD, with xt) Non-OECD Countries, N=29 34 2.29 Persistence and Average Inflation: HP, with xt, Non-OECD Countries, N=29 34 2.30 Persistence and Average Inflation: QTD, with xt, Non-OECD Countries, Excluding Episodes of Hyperinflation 34 2.31 Persistence and Average Inflation: HP, with xt, Non-OECD Countries, Ex-cluding Episodes of Hyperinflation 35 2.32 Persistence and Average Inflation: QTD, with xt, Non-OECD Countries, Excluding Argentina, Brazil, and Israel 35 2.33 Persistence and Average Inflation: HP, with xt, Non-OECD Countries, Ex-cluding Argentina, Brazil, and Israel 35 2.34 Persistence and Average Inflation: AR(2), HP, with xt, Non-OECD Coun-tries, N=29 35 2.35 Persistence and Average Inflation: AR(2), HP, with xt, Non-OECD Coun-tries, Excluding Episodes of Hyperinflation 36 2.36 Persistence and Average Inflation: AR(2), HP, with xt, Non-OECD Coun-tries, Excluding Argentina, Brazil, and Israel 36 2.37 Persistence and Average Inflation: HP, N=51 38 2.38 Persistence and Average Inflation: QTD, N=51 38 2.39 Persistence and Average Inflation: The Inverted-U Relationship, HP, N=51 38 2.40 Persistence and Average Inflation: The Inverted-U Relationship, QTD, N=51 39 2.41 Persistence and Average Inflation: Excluding Episodes of Hyperinflation, HP, N=51 40 2.42 Persistence and Average Inflation: Excluding Episodes of Hyperinflation, QTD, N=51 40 2.43 Persistence and Average Inflation: Excluding Argentina, Brazil, and Israel, HP, N=51 40 2.44 Persistence and Average Inflation: Excluding Argentina, Brazil, and Israel, QTD, N=51 44 2.45 The Inverted-U Relationship: Excluding Episodes of Hyperinflation, HP, N=51 44 2.46 The Inverted-U Relationship: Excluding Episodes of Hyperinflation, QTD, N=51 44 2.47 Alternative Measures: Full Sample, HP 45 2.48 With Country Specific Characteristics: Dependent Variable = 0, QTD . . . 45 2.49 With Country Specific Characteristics: Dependent Variable = 0, QTD . . . 46 3.1 Real Exchange Rate Persistence and Trend Inflation: Full Sample 56 3.2 Real Exchange Rate Persistence and Average Inflation: Full Sample . . . . 56 3.3 Episodes of Hyperinflation _ 58 3.4 Real Exchange Rate Persistence and Trend Inflation: Excluding Episodes of Hyperinflation 61 VI 3.5 Real Exchange Rate Persistence and Average Inflation: Excluding Episodes of Hyperinflation 61 3.6 Real Exchange Rate Persistence and Trend Inflation: Excluding Argentina, Brazil, and Israel 62 3.7 Real Exchange Rate Persistence and Average Inflation: Excluding Argentina, Brazil, and Israel 62 3.8 Real Exchange Rate Persistence and Trend Inflation: OECD Countries . . . 63 3.9 Real Exchange Rate Persistence and Average Inflation: OECD Countries . 63 3.10 Real Exchange Rate Persistence and Trend Inflation: Non-OECD Countries 63 3.11 Real Exchange Rate Persistence and Average Inflation: Non-OECD Countries 64 3.12 Real Exchange Rate Persistence and Trend Inflation: Non-OECD Countries, Excluding Episodes of Hyperinflation 64 3.13 Real Exchange Rate Persistence and Average Inflation: Non-OECD Coun-tries, Excluding Episodes of Hyperinflation • 64 3.14 Two-Stage Estimation: Dependent variable is pi 66 3.15 Volatility of Real Exchange Rates and Average Inflation 67 4.1 Calibration 84 4.2 Contemporaneous Correlations 86 4.3 Relative Volatility 86 4.4 Steady-State Shares 96 vii List of Figures 2.1 Argentina: Actual and HP-Trend Inflation (dotted line) Rates 24 2.2 Brazil: Actual and HP-Trend Inflation (dotted line) Rates 25 2.3 Israel: Actual and Trend Inflation Rates 26 2.4 Full Sample 41 2.5 Excluding Episodes of Hyperinflation 42 2.6 Excluding Argentina, Brazil, and Israel 43 3.1 Argentina: Actual (dark line) and Trend Inflation Rates (1973-1996) . . . . 58 3.2 Brazil: Actual (dark line) and Trend Inflation Rates (1973-1996) 59 3.3 Israel: Actual (dark line) and Trend Inflation Rates (1973-1996) 60 4.1 Impulse Response of Output: Slow Vs. Instantaneous Diffusion 89 4.2 Impulse Responses: 7 = 0.8, Sn = 0.025 90 4.3 Impulse Responses: 7 = 0.8, Sn = 0.025 91 4.4 Impulse Responses: 7 = 0.64, Sn = 0.025 92 4.5 Impulse Responses: 7 = 0.64, Sn = 0.025 93 4.6 Devereux, Head, Lapham Model (1996) 94 v n 1 Acknowledgement I would like to thank my thesis committee; Paul Beaudry, Michael Devereux, and Jim Nason. Without their suggestions, guidance, and encouragement this thesis never would have been completed. There are a number of individuals who also took the time and effort to read various versions to the work in this thesis to whom I am also grateful; Joel Bruneau, John Cragg, Francisco Gonzalez, Rahat Kurd, Lonnie Magee, Angela Redish, Christian Sigouin, Alan Stark, Jim Storey, and Lasheng Yuan. I must also acknowledge the help and comments I received from participants in U.B.C.'s. Graduate Student Seminars, U.B.C.'s Macro-Lunch Workshops and the Canadian Economic Association Meeting (1997). Anna Comfort, Oliver Sea, and Michael Winsemann deserve special thanks for their help and support at critical stages of this thesis. Last, but certainly not least, without the love and encouragement of my family I never could have reached this stage. - I X C h a p t e r 1 Introduction A major challenge for macroeconomists is to explain the persistent nature of output and real exchange rate fluctuations observed in the international data1. Expansions and contractions in economic activity, as summarized by deviation of national output from its long run growth path, usually last, for several years. Similarly, the real exchange rate (nominal exchange rate adjusted for price levels) displays large and persistent deviations from Purchasing Power Parity (PPP) 2 . In the literature, there are two main approaches to explain these stylized facts. The first approach emphasizes aggregate demand shocks (for example, monetary shocks) as the driving force behind these fluctuations. This approach gives nominal price stickiness a central role. Nominal price stickiness or "sticky prices" can occur if firms face small fixed costs associated with changing the price of their products3. The explanation based on sticky prices, as a channel for persistent fluctuations in output, is as follows. In the presence of menu costs associated with price changes, it is optimal for firms to leave prices unchanged in response to some demand shocks and change output instead4. If different, firms change prices at different times so that pricing decisions are staggered, the aggregate price level is slow to adjust,5. Therefore, aggregate output, ^ee, for example, Campbell and Mankiw (1989), Mussa (1986), and Froot and Rogoff (1995). 2According to the theory of PPP, the real exchange rate should be constant. 3Akerlof and Yellen (1985) and Mankiw (1985) rationalize the existence of sticky prices as an outcome of profit-maximizing behaviour of firms in the presence of small fixed costs, typically referred to as "menu costs". 4For firms to be willing to supply more output at the same price they must have some monopoly power. That is, price should be greater than marginal cost. 5The seminal work of Taylor (1979, 1980) demonstrates the importance of overlapping (or staggered) wage contracts as channel which can lead to persistent effects of monetary shocks. Blanchard (1983) shows how staggered pricing decisions of firms can lead to inertia in the aggregate price level if individual price setters are averse to changes in relative prices. 1 deviates from its long-run growth path in a persistent manner. Likewise, the explanation based on sticky prices, for persistent deviations of real ex-change rate from PPP, is as follows. Monetary shocks cause a change in the nominal exchange rate. If national price levels are slow to adjust when prices are sticky, the real exchange rate will deviate from PPP for potentially extended periods of time. The second approach emphasizes aggregate supply shocks as the driving force behind output fluctuations. Under this approach, prices are assumed to be perfectly flexible and the transmission of shocks is via real propagation mechanisms. Some examples of these real mechanisms include labour hoarding, increasing returns, and learning by doing. The explanation for persistent output fluctuations based on these mechanisms has met with varying degrees of success6. This thesis comprises three essays. In the first essay (chapter 2), I test a cross-sectional prediction of the sticky price models for output dynamics. In the second essay (chapter 3), I test a cross-sectional prediction of the sticky price models for real exchange rate dynamics. In the third essay (chapter 4), I develop a structural dynamic general equilibrium model (DGE) model to explore the role of slow diffusion of new products as a potential real propagation mechanism. I discuss the contents of these essays below. 1.1 T h e C o n t r i b u t i o n of Th i s Thesis In high inflation countries the frequency of price adjustment is expected to be high. Ac-cording to Taylor (1998, Pg. 25-26), The frequency of wage and price changes depends on the average rate of in-flation....prices at small businesses, industrial prices, and even the prices of products like magazines are adjusted more quickly when the rate on inflation is higher. This dependency of price and wage setting on events in the economy is one of the more robust findings....Moreover, we have no empirical evidence that 6See, for example, Burnside, Eichenbaum (1996), Beaudry and Devereux (1995), Perli (1998), and Cooper and John (1999) 2 anything other than a change in the inflation rate would change the frequency of price and wage adjustment, though one would expect legal or technological changes that increase the cost of changing prices would reduce price adjustment frequency. For a given average inflation rate, constant frequencies of price ad-justment may not be a bad assumption to make in empirical or policy model. That is, when prices of all goods (whether inputs or outputs) in an economy are rising, firms experience rapid changes in their relative prices. Therefore, they are less inclined to hold their price unchanged. This observation implies that the duration of the price contracts should be small in high inflation countries. Consequently, the staggering of pricing decisions, which generates inertia in the adjustment of aggregate price level, is weak. The staggering of pricing decisions is the essential ingredient in the models which address the issue of persistence in output or real exchange rate fluctuations. The opposite should be true for low inflation countries. The systematic difference in price stickiness across countries yields testable predictions of sticky price models for persistence in output and real exchange rate fluctuations. The work of Lucas (1973), and Ball, Mankiw, and Romer (1988) among several others, has demonstrated the usefulness of testing cross-sectional predictions of macroeconomic theories to assess their relevance. The first and second essays of the thesis are in this tradition. Romer (1990) presents a formal static model to highlight the endogenous nature of price stickiness. He shows that price stickiness is inversely affected by the trend inflation rate. Dotsey, King, and Wolman (1998) develop a DGE model with richer price setting rules. In this model the degree of price stickiness depends on the state of the economy captured by the trend inflation rate7. T h e focus of Romer's model is on time-dependent pricing rules. Under this type of pricing rules the duration for which firms keep their prices unchanged is a fixed time period. An increase in the trend inflation rate would lead to a shortening of this fixed time period. Dotsey, King, and Wolman (1998) on the other hand combine the time-dependent pricing rules and state-dependent pricing rules. Under the latter, the decision to keep prices unchanged depends on the state of the firm, industry and/or the economy. 3 In the first essay I test the prediction that deviations of output from its trend should be less persistent in high inflation countries. I use IFS data for 51 countries over the period 1950 - 1996. The results of this essay reveal that the inverse relationship between persistence in output deviations and trend inflation is not statistically significant. The same result holds when I restrict attention to OECD countries. The empirical analysis suggests that it is important to take into account the time variation in inflation within individual countries in cross-country studies. In particular, the ideal environment to test the cross-sectional predictions of the sticky price models should have two features. First, there should be high cross-sectional variablity in inflation rates. Second, countries should be at stable levels of inflation. That is, there should be little time variation in inflation within countries. A feature of the existing data is that the countries with high inflation are also the ones with high time variability of inflation. As such, using average inflation as a summary measure of inflationary experience may obscure the influence of time variation within countries. I address this issue in two ways. First, I identify the inflationary environment by the long-run movement in inflation, or the trend inflation rate. Second, I take the minimalist, approach to reduce the high time variability within countries by eliminating episodes of hyperinflation. In this manner, the empirical implementation is better able to test the predictions of the model. For instance, in the full sample, I find that, the inverse relationship between persis-tence in the deviation of output from trend and average inflation is statistically significant. However, the exclusion of episodes of hyperinflation in only 3 out of 51 countries (namely Argentina, Brazil, and Israel ) renders this relationship statistically insignificant. The episodes constitute less than 1% of the entire panel data. In the second essay, I test the prediction that, deviations of real exchange rate from PPP should be less persistent in high inflation countries. I use IFS data for 49 countries over the period 1972 - 1996. The results of this essay reveal that the inverse relationship between persistence in real exchange rate fluctuations and trend inflation is extremely fragile. I find that, the inverse relationship is statistically significant, only if the episodes of 4 hyperinflation in Argentina, Brazil, and Israel are included in the estimation. As argued above, the exclusion of these episodes to reduce time variation in inflation within countries is desirable. Once these episodes are excluded the relationship predicted inverse relationship is statistically insignificant. When I restrict attention to OECD countries I once again find statistical insignificance. The results from the two essays suggest that only episodes of hyperinflation, which are periods of extreme monetary instability, are informative as far as the predictions of sticky price model for output and exchange rate dynamics are concerned. The lack of a relation-ship between trend (or average) inflation and persistence in either output or real exchange rate fluctuations is difficult to reconcile with the staggered sticky price framework. In fact, one has to be willing to assume that price stickiness is inelastic with respect to average inflation over a very broad range of average inflation- from 2-3% to 60-70%. The sticky price framework has been developed as a microfoundation for explaining persistent output and real exchange rate fluctuations. Therefore, the lack of support for the predictions in the international data raises a problem for this framework. In the third essay, I construct a multi-sector DGE model calibrated to U.S. data. In this model, there is a monopolistically competitive intermediate good sector where each firm produces a unique intermediate product. In another sector of the economy, new products are created using real resources. Since the range of products in the model economy maps one-to-one with the number of firms, new products are introduced by way of entry of new firms. The diffusion of new products in the economy raises aggregate productivity8. However, the diffusion is not instantaneous. I explore the role of slow diffusion of new products in propagating the shocks to the economy. Aggregate output in the model depends both on the firms' output (intensive margin) and the range of products in the economy (extensive margin). I find that, in contrast to a model of Devereux, Head, and Lapham (1996) in which there is there is instantaneous diffusion of new products, the response of output to technology shocks displays a characteristic hump-shape as observed in the U.S. 8 The classic paper by Romer (1987) uses this mechanism to study endogenous growth. 5 data9. In the model, a positive productivity shock not only enhances current output but also leads to the creation of new products. Upon being diffused in the economy, these new products raise aggregate productivity. The key implication of the multi-sector set up is that consumption and employment move together after the period of initial shock. In models with weak internal propagation, consumption and employment move in opposite directions after the initial period of shock10. The results from this essay suggest that slow diffusion of new products may be a potential real propagation mechanism that warrants further quantitative investigation. 9Devereux, Head, and Lapham (1996) address the issue of measurement of technology shocks. 1 0 An exception is the model by Perli (1998). 6 C h a p t e r 2 Price Stickiness, Inflation, and Output Dynamics: A Cross-Country Analysis A class of business cycle models that emphasize aggregate demand driven fluctuations (in particular via monetary shocks) give price stickiness a central role1. Price stickiness may arise, for example, in the presence of small fixed costs (typically referred to as "menu cost") associated with adjusting nominal prices2. Therefore, in response to some aggregate demand shocks firms may choose to keep their prices unchanged and respond instead by making adjustments in output. When such pricing decisions are staggered across firms, the aggregate price level is slow to adjust and therefore demand shocks may cause output to persistently deviate from its long run growth path. The duration for which a firm keeps its price unchanged may itself depend on the underlying state of the economy such as the trend inflation rate3. A high trend inflation rapidly erodes the real price of a firm's output and therefore induces frequent revisions in its nominal price and correspondingly less adjustment in output. Thus the extent to which price stickiness can lead to persistence in output fluctuations depends inversely on trend inflation. This observation suggests that a business cycle model which emphasizes price stickiness as a mechanism to generate persistence in output fluctuations has the following implication: Nominal price stickiness should be less important in countries with high trend inflation relative to countries with low trend inflation. Therefore, deviations of output from, its long T h e work of Fisher (1977), Taylor (1979, 1980), Sheshinski and Weiss (1977, 1983), Blanchard (1983), Calvo (1983), Mankiw (1985), Akerlof and Yellen (1985), Blanchard and Kiyotaki (1987) has provided the microfoundations for a theory of demand driven aggregate fluctuations. 2Akerlof and Yellen (1985) and Mankiw (1985) show how price stickiness may arise as an outcome of profit-maximizing behaviour by firms. 3Romer (1990) formalizes this idea. He combines the two approaches to staggered pricing, namely, the time-dependent and the state-dependent pricing structures in a static general equilibrium model. Dotsey, King, and Wolman (1998) accomplish this task in a dynamic general equilibrium framework. 7 run growth path should be less persistent in high trend inflation countries relative to low trend inflation countries. The objective of this paper is to examine this implication empirically. The work of Lu-cas (1973) and Ball. Mankiw, and Romer (1988) among several others has demonstrated the usefulness of testing cross-sectional predictions of macroeconomic theories. The present chapter is in this tradition. I use annual data from 51 countries to investigate the relation-ship between trend inflation and persistence in output. In the empirical implementation I pay particular attention to the issue of within-country time variation in the trend infla-tion across countries. From the point of view of empirical implementation, a high time variability of inflation within a country is an undesirable feature. I, therefore, employ two separate methods to control for this time variability. First, I identify the inflationary en-vironment within a particular country by the long-run movement in its inflation rate. I refer to this as the trend inflation rate. Second, I reduce the high time variability within a country by excluding periods of extreme monetary instability. I refer to such periods as episodes of hyperinflation. In this manner, the empirical implementation is better able to test the hypothesis. I use both the time- and the cross-sectional dimension of the data in the estimation. My estimation results do not support the hypothesis that high trend inflation countries have less persistent output fluctuations. When the time variation is ignored, and average inflation is used to characterize the inflationary environment within a country, the data lends weak support to the hypothesis. In this particular case I argue that it is more likely that the inverse relationship in the data is due to factors other than the price stickiness mechanism. For the exclusion of a few episodes of hyperinflation identified in Argentina, Brazil, and Israel makes the relationship between persistence and average inflation statis-tically insignificant. These hyperinflationary episodes constitute less than 1% of the entire panel data. The empirical results of this paper have important implications. First, the sticky price models are used as the microfoundation for an environment which can generate persistent 8 effects of aggregate demand shocks ( See, for example, the early work of Taylor (1980), and more recently, Jeanne (1998), Bergin and Feenstra (1998))4. The lack of empirical support for a key prediction of this class of models suggests that while these models are important environments in which one can study the impact effects of monetary policy innovations, they may be less useful in explaining the persistence of monetary shocks. Second, one has to make the assumption that persistence in output fluctuations is inelastic with respect to average inflation rate over a very broad range - from 2% - 3% to 60% - 70%. Moreover, only periods of extreme monetary instability are informative about the prediction of the sticky price model examined here. Such a position seems intuitively unappealing. 4Chari, Kehoe and McGrattan (1998a) implement Taylor's (1980) staggered pricing structure in a D G E model. They find that contrary to Taylor's insight, the staggered pricing structure can generate persistent real effects of monetary shocks only if one assumes that prices are exogenously sticky for a long period of time ( about 2 | years). The intuition behind their result is that if firms choose not to change the price of their product then price must not be very sensitive to changes in marginal costs. A requirement forHhis to occur in their D G E model is to have preferences with zero income effects (so that the labour supply response is not dampened) and implausibly high labour supply elasticity (flat labour supply curves). This result has questioned the ability of the sticky price framework to generate persistent effects of monetary shocks. In response, several recent papers show that Chari, Kehoe, and McGrattan's result is particular. Bergin and Feenstra (1998) are able to generate persistent output dynamics by making two modifications to the model of Chari, Kehoe, and McGrattan (1998a). First, they introduce translog preferences instead of CES. And secondly, they allow for an input-output structure where a firm's inputs are other firms' output. The implication of the first modification is that price setting rules are not a simple mark up over a firm's own marginal cost, but rather, they are influenced by other firms' prices. This interaction introduces strong linkages in price setting rules across firms. The second modification implies that output prices of firms become an important component of marginal cost thereby reducing the importance of labour input. Likewise, Jeanne (1998) develops a D G E model where there is an interaction between product market nominal rigidity (sticky prices) and labor market real rigidity (efficiency wages). Jeanne builds on the static model of Ball and Romer (1990) who show that the presence of real rigidities can enhance the effect of nominal rigidities. He confirms the result of Ball and Romer (1990) in a D G E model. The period for which prices must remain sticky in order to generate quantitatively important persistence in output can be reduced substantially to 3 quarters. Finally, the papers by Anderson (1998) and Huang and Liu (1998) emphasize the differences between staggered wage and staggered price contracts. Huang and Liu (1998) show that a key parameter governing the persistence properties in staggered wage (price) contract models is the elasticity of relative wage (price). The smaller the value of this parameter, the smaller is the response of wages to demand shocks, the less is the need to revise price, and the greater is the persistence in output. For staggered wage models this elasticity turns out to be small whereas for staggered price model such as that in Chari, Kehoe, McGrattan (1998a) it is large. 9 Previous empirical research has focused on the contemporaneous output-inflation trade-off or the impact effects of aggregate demand shocks on output5. In particular, Ball, Mankiw, and Romer (1988) find that the impact effect of aggregate shocks is smaller in countries with high inflation. This finding is interpreted as evidence in favour of the sticky price models. Kiley (1998) examines, as I do, the issue of price stickiness and business cycle persistence. However, my conclusions are very different. Using the updated Ball, Mankiw, Romer (1988) data set, he finds that price stickiness decreases with average inflation across countries and interprets this finding as strongly supportive of the propagation mechanism based on sticky price (menu-cost) models. Kiley (1998) ignores the time variation in inflation across countries. I argue that taking account of this time variation is important, for an accurate empirical implementation of the theory. Further, in the particular case where there is support, for the hypothesis, I find a statistically significant inverted-U relationship between persistence and average inflation. Such a relationship is at variance with a clear-prediction of the sticky price model. The outline for this paper is as follows. In Section 2.2, I describe the theoretical framework for my empirical analysis. In Section 2.3, I discuss the empirical implementation issues and the methodology. In Section 2.4, I present the main results. In Section 2.5 I present the results for OECD and Non-OECD countries. The results from an alternative methodology - two-stage estimation - are presented in Section 2.6. Finally, Section 2.7 gives concluding remarks. 2 . 2 Theoretical Framework In this section I describe the theoretical framework underlying my empirical analysis. On the supply side, there is a unit, mass of monopolistically competitive firms. A convenient, way to introduce staggered price adjustments is by employing the price setting structure of Calvo (1983). Under this pricing structure, each firm can adjust its price in a given period 5For example, Lucas (1973), Alberro (1981), Ball, Mankiw, and Romer (1988), Defina (1991) and Koelln, Rush, and Waldo (1996) 10 with probability 1 — 0. Therefore, with probability 0, a firm charges the predetermined nominal price and satisfies the demand forthcoming at that price. This probability is assumed to be independent across time and identical across firms. The symmetric market structure implies that all firms that change their price charge the same price. The average duration for which the price quotation of a firm stays unchanged is jz^- At any time, the fraction of firms that adjusted their price k periods ago is given as 9^ = (1 — (j))(j)k. The aggregate price level takes the form6 oo Pt = {^{PU)l-e)^- (2-1) k=0 In the above expression, P*_k is the optimal price chosen by a firm k periods ago and e is the elasticity of demand. Using the expression for Ok and (2.1), the aggregate price level in a symmetric equilibrium can be shown to take the following recursive form pt = [ ( i - 4>){Pt)l-e+m-i)1-*}^- (2.2) This expression shows that the aggregate price level has two components. First, a fraction, l — 4>, of firms charge the optimal price P£ at time t. Second, the remaining fraction of firms (j), charges the predetermined price Pt-i- Thus, the aggregate price level in equilibrium is completely characterized by {Pt*,Pt-i}. Another advantage of this set up is that it allows for an arbitrary degree of price rigidity. For instance, if 4> = 1 it indicates that prices are completely rigid. If <fr = 0 then prices are completely flexible. Therefore, the degree of nominal rigidity is given by the parameter </>. The inflation rate is given as irt = — ^ I represent the aggregate demand of the economy as yt = m,t-pt, (2.3) where yt = log(Yt), mt = log(Mt), and pt = log(Pt) are real output, nominal demand, and the price level in logs respectively. This relationship can be obtained from a representative 6 A few selected examples of dynamic general equilibrium models with staggered pricing are Yun(1996), Woodford (1996), Rotemberg(1996), King and Wolman (1996, 1998), Goodfriend and King (1997), Dotsey, King, and Wolman (1998). Cooley and Hansen (1995) explore the role of monetary shocks within a real business cycle set-up. 11 consumer's optimization problem in which the consumer must hold money to finance pur-chases. The nominal demand, mj, in equation (1) is equal to nominal money stock7. The driving process is the rate of growth of money stock jit, which is assumed to follow IH = ft + PmlM-l + e-m,t, emt ~ i.i.d.(Q, cr^t). (2.4) In the staggered pricing environment described above, Jeanne (1998) shows that the devi-ations of output from trend, yf = yt — yj', takes the form y1; = ^ )ytl + ^ {4>)pt, (2-5) In equation (2.5), pt represents the monetary growth. The coefficient $(</>) characterizes persistence in output where the degree of nominal rigidity, <fi is fixed. The relationship between persistence parameter and cfi is given as That is, an increase in the fraction of firms which keep their prices fixed leads to an increase in the persistence of output deviations. Alternatively, an increase in 1 — (p w i H lead to an increase in the average duration for which a firm's price is fixed. Therefore, the firm responds by adjusting its output. In the Calvo (1983) framework, the probability of a price change, <p, is exogenously fixed. Romer (1990) endogenizes this frequency in terms of the underlying features of the economy <£ = < X 7 r T , a L ^ O , (2-7) where irT is the trend inflation rate8, cr^ , is the variability of nominal shocks, and F is the fixed cost of changing prices, and K can be interpreted as the degree of real rigidity in 7 The two assumptions underlying this formulation are: 1) Money demand distortions due to positive nominal interest rate are negligible. 2) Fiscal policy is in the form of lump-sum taxes and transfers. sIn equilibrium, the trend inflation rate is linked to the exogenous trend growth in the money stock. 12 the market. Further that9, d * < 0. (2.8) Therefore, a rise in trend inflation decreases the average duration for which prices are fixed. To summarize, the theoretical framework described above shows that a higher trend inflation will increase the frequency of price adjustments among firms. Therefore, a larger-fraction of the firms in the economy adjust prices in response to demand shocks. The fraction of firms that does not change prices adjusts output. This fraction decreases with an increase in trend inflation leading to a less persistent deviation of output from its trend. The implication of this result for my cross country analysis is that a country with a high trend level of inflation should exhibit less persistent deviations of output from its trend as compared to a country with a low trend level of inflation. 2.3 Empirical Implementation I postulate an empirical counterpart of equation (2.5) where detrended output follows a general second-order linear process: vi = *H<Kf$Ut)))yLi + *2 W(n«)))y2_2 + *(0(/(n f t)))/z i t + ult, (2.9) where (i denotes the country) i = 1,...,N and t = l, . . .Tj. yft is the detrended output for country i. The term f(Hit) denotes the inflationary environment within country i. pa In Romer's (1990) model each firm chooses the probability of adjusting (or equivalently probability of not adjusting) its price taking as given the other firms' decisions. In equilibrium, due to the symmetry, all firms choose the same probability of adjusting their nominal price. Factors other than the trend inflation rate influence a firm's choice in the following manner _ ^ _ < 0 ^ > 0 ^ > 0 dal ' dF ' • dK More recently, Dotsey, King, and Wolman (1998) provide a synthesis of both time-dependent pricing and state-dependent pricing in a dynamic general equilibrium framework. The staggered pricing structure in their paper is richer for it allows 4> to be firm specific. Thus, at any given point in time, there are different vintages of firms according to the time they last adjusted their price. In this environment, the probability of price adjustment rises with an increase in the steady state inflation or the trend inflation rate. 13 represents fluctuations in aggregate demand. The error term un captures other sources of fluctuations in output such as supply shocks. The empirical implementation of the hypothesis that countries with high trend inflation rate have low persistence in output fluctuations around their trend raises several important issues. The ideal experiment for testing the cross-sectional implication of the theory is to have a set of countries with different levels of steady inflation rates. In other words, a high cross-sectional variation and minimal within-country variation in inflation would be a desirable feature of the data. It could then be assumed that the same sticky price model applies to individual countries and that differences in inflation across countries lead to different outcomes. Unfortunately, the countries that have high average inflation have also experienced enormous time variation in inflation. The empirical analysis should take into account this time variation or the changes in the inflationary environment of individual countries. By reducing this within-country variation the empirical implementation better able to test the theoretical prediction of the model. One way to reduce this time variation within countries is to consider the long run movements in inflation. A second way is to exclude periods of extreme time variation - that is, episodes of hyperinflation within countries. I discuss the latter issue in the next section. I consider two representations of the inflationary environment /(Ii?;t) /(Hit) = : the long-run (trend) inflation rate, : the average inflation rate. I obtain the long-run component of inflation ir[t in two separate ways. First, I use the HP filter to extract the short-run (high-frequency) component of inflation. Upon subtracting this short-run component from the actual inflation rate I obtain the long-run or trend inflation rate. Second, I identify the long-run component of inflation as the quadratic time fitted value of inflation. I also use average inflation to emphasize the consequences of adjusting for time variation in inflation. Both the long-run (trend) inflation and the average inflation rates serve as the description of the inflationary environment within which I want 14 to test the implication of the sticky price model. An advantage of panel estimation is that it allows me to explicitly take into account the long run movements in inflation. The data on a monetary aggregate that captures the shifts in the stance of mone-tary policy - one source of aggregate demand shocks - is not available for most countries. Therefore, following other related studies in this literature, I use nominal output growth as the measure of exogenous aggregate demand fluctuations. I also obtain a measure of unanticipated nominal output growth that represents shocks to aggregate demand. f xn : nominal output growth rate, (2 11) xftA : unanticipated nominal output growth. I assume a rational forecasting rule to obtain the unanticipated nominal growth for each country. I obtain xftA as the residual from the regression of xu on a constant, xa-i, and Xit-2-To obtain the cyclical component of real output (yft) I use the HP filter (HP) and quadratic time detrending (QTD). These procedures are extensively used in the business cycle literature. The functions $ l ((/>(.)) and $2(0(.)) reflect that the trend inflation affects the dynamic behaviour of output by influencing the frequency of price adjustment. The term ($(.)) captures the impact effect of nominal demand shocks. I take a linear approximation of these functions to obtain the following specification yi = a + + $ l x / ( n , ; t ) 4 - i + *fait-2 + ^ 7 ( n , ; t ) 4 - 2 + *ofMt + ^ / ( f l , , W + ult. (2.12) This specification has the advantage that it nests both the impact effect and the persistence in output fluctuations due to aggregate demand shocks. In my analysis I consider both AR(l) and AR(2) output dynamics. I describe the measure of persistence for the AR(1) case below. 15 2.3.1 AR ( 1 ) Output D y n a m i c s In the case of AR(1) output dynamics, I restrict the coefficients $ 2 1 = 0 and "I"2, = 0 in equation (12). Writing it in the stacked form to obtain y t d = a + Qfcti + ^ 1 f (n t )y t d _ 1 + *o^t + ^ f ( n t ) y u t + u t . (2.13) The definition of persistence in output that I consider in this section is: how closely is the deviation of output from its trend in the current period related to the deviation of output from, its trend in the previous period. That is, - ^ = $£ + $^(110. (2.14) I am interested in examining how the inflationary environment affects persistence in output, that is, the cross-partial: d ^ =<e (2.i5) af(n t)(a y d_ 1; Therefore, the coefficient of the interaction variable of inflationary environment and lagged output is of central interest. The class of nominal rigidity models with staggered price setting among firms imply that, an increase in the trend inflation rate will make firms adjust their prices more frequently and, therefore, make less adjustment in output. Thus, deviations of output from its trend will be less persistent. The theoretical prediction of this class of models is that ^ l should be negative. As mentioned earlier, the focus of a large body of previous research, with the exception of Kiley (1998), has been on the impact effect of aggregate demand shocks. In my empirical specification, the impact effect is captured by the coefficients <J/o and tyn as ^ = *o + * T f(n t ) . (2.16) In particular, the influence of the inflationary environment on the impact effect of aggregate demand shocks is given by d(dy?) 0f(n t)(dy t) (2-17) 16 Sticky price models predict that tyn should be negative. That is, the impact effect of aggregate demand shocks should be less in high inflation countries. Ball, Mankiw, Romer (1988) test this prediction. I estimate the following specification for the panel of 51 countries allowing for cross-sectional heteroscedasticity. yft = a + + ^ mMt-i + *olMt + ^m^fHt + iHt- (2.18) Defining [f(Uu) * yft-i Pi* ^ulM.t[ = -^2,it I can write the above equation as: yi " I yi ^2 ,1 = * i yL X2,51 a + U l U 5 1 where y ; = [yii...yiTi}', yj = [yio-yiTi-iY, and u; = [ u i l . . . u i T i } / , The above can be compactly written as y = X$ + u. The covariance matrix is given as: £[uu'] = fl where = E N X N ^ITIXTI • The off-diagonal elements of the Q, matrix are all zeros due to the unbalanced nature of the data. I allow for cross-sectional heteroscedasticity thus Diag(Y,) = [S1...E51]'. I conduct Feasible GLS estimation to obtain the parameter estimates $ = (x ' f i - 1 x)- 1 x / n- A y, (2.19) Ti 2.3.2 Data The sample consists of annual IFS data on real and nominal GDP/GNP for 51 countries. The overall sample period is 1950-1996. The inflation rate is obtained as the growth rate of the GDP deflator. The Data Summary section at the end of this chapter provides 17 information on individual countries, the respective sample period, and the average inflation rate. The dataset includes the 43 countries in the Ball, Mankiw, Romer (1988) study10. I expand the dataset by including eight more countries. These countries are South Korea, New Zealand, India, Pakistan, Paraguay, Thailand, Malaysia, and Kenya. 2.4 Results I first present the results for the case where I estimate a simplified version of 2.18 which puts minimal structure on the regression. The results are for the entire panel of 51 countries. For all the Tables the term 'HP' denotes HP filtered output data, the term 'QTD' denotes quadratic time detrended output data. As mentioned above, I use both HP and QTD methods for obtaining the long-run trend inflation rate. For the HP filtered output data I use long-run inflation obtained from the HP filter and for the QTD output data I use the quadratic time trend inflation, respectively. The p-value shows the exact significance level below which the null hypothesis (Ho : $ 1 1 = 0) cannot be rejected. V denotes that the coefficient is statistically different from zero at the 5% level of significance. yft = a + Qlyi^ + $ i V ( n 7 ; t ) 4 - i + iHt. (2.20) In Tables 2.1 and 2.2 the inflationary environment of a country is captured by its long-run or trend inflation rate whereas in Tables 2.3 and 2.4 I use the average inflation rate. The results in Tables 2.1 and 2.2 indicate that the coefficient of interest, $ 1 : L, is sta-tistically insignificant at the 5% level for both the QTD and HP cases. For the HP case, even the sign of the coefficient is positive which is opposite from the predicted one. These results indicate that when within-country time variation in inflation is taken into account, the trend inflation rate does not influence persistence in output fluctuations. 1 0 I thank Michael Kiley for generously providing the updated Ball, Mankiw, Romer dataset. In the data series for three countries, namely, El Salvador (Real GDP), Netherlands (Nominal GDP), and Switzerland (Nominal and Real GDP). I found a discrepancy between the data received from Michael and the series obtained from the IFS Database. I use the IFS series for the respective variables. 18 Table 2.1: Persistence and Trend Inflation: QTD Coeff. Std. Error p-value 0.833* 0.017 0.000 -0.169 0.110 0.104 Constant -0.0002 0.0005 0.723 ?able 2.2: Persistence and Trend In lation: H Coeff. Std. Error p-value 0.714* 0.020 0.000 0.009 0.109 0.929 Constant -0.00001 0.0005 0.977 When I use the average inflation rates to characterize the inflationary environment within countries I find that for QTD data there is support for the hypothesis. The coefficient cfr11 is negative and statistically significant in Table 2.3. This result suggests that in countries with high average inflation rates the persistence in output deviations from trend is less as compared to countries with low average inflation. Such a conclusion is supportive of the sticky price model which is designed to explain persistent output fluctuations. I argue that the empirical support for the model in this particular case is extremely fragile for two reasons. First, in the HP filtered data, the coefficient is statistically insignificant (see Table 2.4). Therefore, the empirical support for the hypothesis is fragile with respect to the methodology used to obtain the cyclical component of output. Second, the empirical support for the hypothesis is fragile with respect to an alternative way of controlling the undesirable within-country time variation. I discuss this latter point in detail in the next section. Table 2.3: Persistence and Average Inflation: QTD Coeff. Std. Error p-value 0.861* 0.020 0.000 $11 -0.434* 0.145 0.003 Constant -0.0002 0.0005 0.704 19 Table 2.4: Persistence and Average Inflation: HP Coeff. Std. Error p-value 0.737* 0.024 0.000 -0.195 0.159 0.221 Constant -0.00001 0.0005 0.983 Table 2.5: Persistence and Trend Inflation: QTD, with xt Coeff. Std. Error p-value 0.833* 0.017 0.000 -0.169 0.110 0.104 ttn 0.064* 0.006 0.000 tt* -0.046* 0.005 0.000 Constant -0.007* 0.0009 0.000 I now present the results for the case where I estimate 2.18. I use the actual nominal output growth, xt, as a regressor to explicitly capture the fluctuations in aggregate demand and its impact effect on output. The results of Tables 2.5 and 2.6 are similar to the results in Tables 2.1 and 2.2. The estimate of coefficient (fr11 is once again statistically insignificant. These results indicate that a higher trend inflation rate does not diminish persistence in output fluctuations. The coefficient that captures the impact effect of aggregate demand shocks, ipn is sig-nificantly negative. Therefore, countries with higher trend inflation do have a lower impact effect of aggregate demand shocks. This result conforms with the finding of previous re-search that has focused on impact effects, in particular, Ball, Mankiw, and Romer (1988). The results for the case when I restrict attention to the countries in the Ball, Mankiw, and Romer (1988) study are qualitatively similar. Similar results hold when I use unanticipated nominal output growth, x^A, to capture fluctuation in aggregate demand and its impact effect(see Tables 2.7 and 2.8). The pattern of results presented in Tables 2.3 and 2.4 is not altered when I introduce nominal output growth, xt, to explicitly capture the impact effects. For QTD data the null hypothesis is rejected at the 5% level. That is, a higher average inflation inversely affects 20 Table 2,6: Persistence and Trend Inflation: HP, with xt Coeff. Std. Error p-value 0.722* 0.020 0.000 -0.093 0.106 0.377 0.077* 0.006 0.000 -0.069* 0.005 0.000 Constant, -0.008* 0.0008 0.000 Table 2.7: Persistence and Trend Inflation: QTD, with x\ Coeff. Std. Error p-value 0.845* 0.017 0.000 *? -0.139 0.104 0.182 0.117* 0.010 0.000 -0.074* 0.007 0.000 Constant, 0.00006 0.0005 0.901 Table 2.8: Persistence and Trend Inflation: HP, with x\ Coeff. Std. Error p-value 0.747* 0.020 0.000 -0.056 0.111 0.612 0.120* 0.009 0.000 -0.110* 0.010 0.000 Constant 0.0001 0.0005 0.713 21 Table 2.9: Persistence and Average Inflation: QTD, with xt Coeff. Std. Error p-value 0.843* 0.020 0.000 -0.305* 0.152 0.045 0.054* 0.006 0.000 ty, -0.064* 0.009 0.000 Constant -0.005* 0.0009 0.000 Table 2.10: Persistence and Average Inflation: HP,with xt Coeff. Std. Error p-value 0.722* 0.024 0.000 -0.069 0.166 0.677 0.047* 0.006 0.000 ty, -0.061* 0.009 0.000 Constant -0.005* 0.0008 0.000 the persistence in deviations of output from its trend. As found in the case without xt, this support for the hypothesis is fragile. For instance, in the case of HP filtered data the coefficient is statistically insignificant. Overall, the results presented in this section bring out the importance of the two is-sues discussed earlier, namely, the within-country time variation in the inflation and the methodology used to obtain the cyclical component of output. 2.4.1 E x c l u d i n g Episodes of Hyper inf la t ion As mentioned earlier a key assumption implicit in examining the hypothesis across countries is that countries are at different levels of steady inflation rates. In the dataset, however, high inflation countries are also the ones with enormous time variation in inflation. Given this feature of the data the question that arises is how can we make average inflation a more appropriate measure of the inflationary environment and, therefore, more appropriate for testing the hypothesis. In this section I pursue the strategy of reducing the within-country time variation by excluding episodes of hyperinflation. I identify periods of relatively stable inflation within the high inflation countries by 22 Table 2.11: Episodes of Hyperinflation Country Period Years 7T Relative Volatility Full Sample 1966-1981 0.977 1.06 4.61 Argentina Unstable 1974-1981 1.653 1.15 5.0 Stable 1966-1973 0.30 0.23 1 Full Sample 1966-1984 0.583 0.51 1.38 Brazil Unstable 1984 2.105 - -Stable 1966-1983 0.499 0.37 1 Full Sample 1971-1996 0.652 0.90 4.09 Israel Unstable 1980-1985 1.983 1.04 4.73 Stable 1971-79, 1986-96 0.252 0.22 1 examining the volatility of inflation in sub-sample periods (see Table 2.11). In Argentina, the relative volatility of inflation in the unstable period is five times that of the stable period. In Israel the relative volatility of the unstable period is 4.7 times that of the stable period. In the unstable periods the inflation rate was in excess of three standard deviations of the average inflation of the stable period11. These unstable periods constitute the episodes of hyperinflation. These episodes are: Argentina (1975 - 1981; 7 observations), Brazil (1984, 1 observation), and Israel (1980 - 1985, 6 observations). These observations constitute less than 1 % of the entire panel data. Figures 2.1, 2.2, and 2.3 show that the inflationary experience of Argentina, Brazil and Israel is marked by episodes of hyperinflation. For these countries, in particular, average inflation may not be a reasonable summary statistic. Moreover, the causes of these hyperinflationary episodes may be linked to institutional changes or drastic shifts in monetary policy. For example, in Israel, the liberalization process that lifted capital controls and introduced foreign exchange indexed accounts triggered the hyperinflationary phase between 1980 - 1986. The results in Tables 2.12 and 2.13 show a drastic change in comparison to the results in Table 2.3 and 2.9. The coefficient $ 1 X is statistically insignificant for the QTD case. For the HP filtered data the coefficient "l?11 not only remains insignificant but also has an "This rule is similar to the one proposed by Tsay(1988) to identify outliers in time series. 23 A r g e n t i n a Brazil Figure 2.2: Brazil: Actual and HP-Trend Inflation (dotted line) Rates 25 Figure 2.3: Israel: Actual and Trend Inflation Rates 26 Table 2.12: Persistence and Average Inflation: QTD, Excl. Episodes of Hyperinflation Coeff. Std. Error p-value 0.824* 0.023 0.000 -0.085 0.187 0.646 Constant -0.0002 0.0005 0.716 Table 2.13: Persistence and Average Inflation: QTD,with xt, Excl. Episodes of Hyperin-flation Coeff. Std. Error p-value H 0.792* 0.022 0.000 0.133 0.19 0.485 tt0 0.134* 0.010 0.000 tt* -0.390* 0.035 0.000 Constant -0.011* 0.001 0.000 opposite sign from prediction of the theoretical model (see Tables 2.14 and 2.15). The results for the case where I exclude the episodes of hyperinflation strongly support my earlier conclusions. That is, the lack of a statistically significant inverse relationship be-tween persistence in output fluctuations and trend inflation in the international data. This finding raises a puzzle for the sticky price model in which the frequency of price changes depends on the inflationary environment. Another aspect of the findings is that suppose one argues that average inflation is in fact an appropriate measure of the inflationary envi-ronment. The results then indicate that the inverse relationship between persistence and average inflation found for the QTD case exists only if one takes into account the peri-ods of hyperinflation. However, theoretical models of price stickiness assume a stable and stationary environment. That is, these models are not about hyperinflationary phenomena. Table 2.14: Persistence and Average Inflation: HP, Excl. Episodes of Hyperinflation Coeff. Std. Error p-value 0.697* 0.027 0.000 0.175 0.214 0.415 Constant 0.00003 0.0005 0.951 27 Table 2.15: Persistence and Average Inflation: HP,with xt, Excl. Episodes of Hyperinfla-tion Coeff. Std. Error p-value 0.676* 0.026 0.000 0.346 0.218 0.112 * 0 0.127* 0.009 0.000 -0.393* 0.034 0.000 Constant -0.010* 0.0009 0.000 In the case where there is support for the hypothesis it is more likely that the inverse relationship arises due to some other factors. For instance, the autocorrelation in QTD output for Argentina is -0.42 and in HP filtered output it is -0.20. If price stickiness indeed disappears at very high levels of trend inflation then the sticky price model predicts that the autocorrelation should be zero and not negative. 2.4.2 A R ( 2 ) Outpu t Dynamics I estimate a more general specification involving AR(2) output dynamics. On the one hand this approach has the advantage that it captures richer output dynamics but on the other, the definition of persistence is more complex. However, the coefficients of the interaction terms on lagged output, <£1:L and <J>21 capture the effect of trend inflation rate on output dynamics12. I directly test for the joint significance of these coefficients. That is, HQ : = 0 and $ 2 1 = 0. The results in Tables 2.16 and,2.17 are for the trend inflation rate. For the HP case, the x2 statistic for the joint test is 1.96 with a p-value of 0.375. This implies that the null of both coefficients being zero cannot be rejected for any significance level below 37.5%. For the QTD case, the x2 statistic is 5.26 with a p-value of 0.09. That is, the null of both coefficients being zero cannot be rejected for any significance level below 9%. 1 2 Due to space limitations I present the result where ji,t = xt. The results for unanticipated demand shocks, fxt = x¥N are qualitatively similar. 28 Table 2.16: Persistence and Trend Inflation: AR(2), QTD Coeff. Std. Error p-value 1.136* 0.026 0.000 *ii -0.276* 0.124 0.026 * H -0.356* 0.026 0.000 ^* 0.104 0.129 0.421 tt0 . 0.056* 0.006 0.000 -0.039* 0.005 0.000 Constant -0.006* 0.0009 0.000 Table 2.17: Persistence and Trend Inflation: AR(2), HP Coeff. Std. Error p-value 0.964* 0.026 0.000 -0.170 0.124 0.172 -0.323* 0.027 0.000 ^* 0.070 0.141 0.619 tt0 0.069* 0.006 0.000 tt* -0.062* 0.005 0.000 Constant -0.007* 0.0008 0.000 29 Table 2.18: Persistence and Average Inflation: AR(2), QTD Coeff. Std. Error p-value n 1.206* 0.030 0.000 $ r r -0.735* 0.168 0.000 -0.399* 0.029 0.000 0.353 0.169 0.037 Constant -0.00005 0.0005 0.914 Table 2.19: Persistence and Average Inflation: AR(2), HP Coeff. Std. Error p-value 1.013* 0.031 0.000 $ i i -0.397* 0.186 0.033 -0.371* 0.030 0.000 $^ 1 0.309 0.1183 0.092 Constant 0.00002 0.0004 0.960 In Tables 2.18 and 2.19 I report the results for the case of average inflation. I find that for the QDT case, the x2 statistic is 19.12 with a p-value of 0.0001. This implies that the null is strongly rejected suggesting a statistically significant relationship between second order output dynamics and average inflation. However, once I exclude the episodes of hyperinflation identified earlier, the result change drastically (see Table 2.19). The x2 statistic value for the joint test is 4.12 with a p-value of 0.127. That is, the null cannot be rejected at any p-value below 12.7%. In Table 2.20 I present the result for the HP case. The x2 statistic value is 5.08 with a p-value of 0.08. That is, the null cannot, be rejected at the 5% p-value but it, is rejected at the 10% level. The exclusion of episodes of hyperinflation give a x2 statistic value of 0.13 with a p-value of 0.936 for the results in Table 2.20. The results for the AR(2) dynamics case are supportive of my earlier results for the AR(1) dynamics case. These results strongly suggest that, contrary to the prediction of the sticky price model, trend inflation does not have any significant, effect, on the persistence properties of output. Further, average inflation appears to have a very fragile negative 30 Table 2.20: Persistence and Average Inflation: AR(2), QTD, Excl. Episodes of Hyperin-flation Coeff. Std. Error p-value n 1.130* 0.036 0.000 -0.100 0.279 0.719 -0.362* 0.036 0.000 0.082 0.272 0.762 Constant -0.00008 0.0005 0.875 Table 2.21: Persistence and Average Inflation: AR(2), HP, Episodes of Hyperinflation Coeff. Std. Error p-value 0.946* 0.037 0.000 0.165 0.288 0.566 n -0.343* 0.037 0.000 0.112 0.289 0.697 Constant 0.00003 0.0004 0.948 influence on persistence. This weak relationship is found to be driven entirely by a few episodes of hyperinflation which are periods of extreme time variation in inflation. 2.5 Output Dynamics: OECD and NON-OECD Countries In this section I divide the countries in the sample into OECD and NON-OECD categories. This separation of countries allows me to ask if the inverse relationship between average inflation and persistence in output fluctuations exists within countries that belong to a particular economic group. The results for the OECD countries are given in Table 2.2213. The OECD countries have experienced less within-country time variation in inflation. This characteristic makes the set OECD countries a more favourable group for testing the hypothesis. 1 3There are 22 O E C D countries in the sample. These countries are indicated in Data Summary table in the Appendix. There exists cross-sectional variability in the average inflation rates within the OECD countries. For example, Canada and US have low average inflation rates of 4.4% and 4.3% respectively whereas Portugal and Iceland have high average inflation rates of 14.5% and 24% over the sample period. The results for the case where unanticipated nominal output growth is used to capture the impact effects are qualitatively similar. 31 Table 2.22: Persistence and Trend Inflation: HP, with xt, OECD Countries, N=22 Coeff. Std. Error p-value 0.629* 0.037 0.000 0.282 0.248 0.528 0.264* 0.016 0.000 ty, -0.700* 0.065 0.000 Constant -0.020* 0.001 0.000 Table 2.23: Persistence and Trend Inflation: QTD, with xt, OECD Countries, N=22 Coeff. Std. Error p-value 0.740* 0.030 0.000 $11 0.104 0.361 0.774 0.245* 0.018 0.000 ty, -0.625* 0.067 0.000 Constant -0.019* 0.001 0.000 I find that neither trend inflation nor average inflation affects the persistence in output fluctuations within the OECD countries. This finding holds for both HP and QTD data (see Tables 2.22 - 2.25). In Tables 2.26 and 2.27 I present the results for the AR(2) case. For both HP and QTD data the null hypothesis HQ : ty^1 = 0, ty2} = 0 is not rejected. The \ 2 t e s t statistic value is 2.46 with a p-value of 0.300 and 1.79 with a p-value of 0.407 for the HP and QDT cases respectively. The results for the case where I consider average inflation are similar. The X2 statistic value is 4.48 with a p-value of 0.11 and 2.97 with a p-value of 0.226 for the HP and QDT cases respectively. These results are not reported here but are available. The Table 2.24: Persistence and Average Inflation: HP, with xt, OECD Countries, N=22 Coeff. Std. Error p-value 0.633* 0.043 0.000 $ i i 0.018 0.268 0.674 -0.234* 0.017 0.000 -0.852* 0.103 0.000 Constant -0.012* 0.001 0.000 32 Table 2.25: Persistence and Average Inflation: QTD, with xu OECD Countries, N=22 Coeff. Std. Error p-value 0.737* 0.037 0.000 0.179 0.481 0.373 tt0 0.233* 0.019 0.000 tt* -0.851* 0.110 0.000 Constant -0.017* 0.001 0.000 Table 2.26: Persistence and Trend Inflation: AR(2), HP, with xu OECD Countries, N=22 Coeff. Std. Error p-value 0.780* 0.047 0.000 0.795 0.546 0.146 -0.224* 0.046 0.000 ^* 0.740 0.527 0.160 tt0 0.245* 0.016 0.000 tt* hline Constant -0.613* -0.019* 0.059 0.001 0.000 0.000 AR(1) and AR(2) output dynamics results strongly suggest that within OECD countries there is no support for the hypothesis. For the Non-OECD countries, the coefficient of interest $ 1 : L is negative for both QTD and HP cases (see Table 2.28 and 2.29). For the QTD case it is statistically significant at the 5% level and for HP case it is almost significant at the 5% level. The three countries within which the episodes of hyperinflation have been identified are all Non-OECD countries. Table 2.27: Persistence and Trend Inflation: AR(2), QTD, with xt, OECD Countries, N=22 Coeff. Std. Error p-value 0.944* 0.047 0.000 *? 0.656 0.538 0.223 -0.247* 0.045 0.000 ^* -0.671 0.515 0.193 0.236* 0.017 0.000 tt* -0.591* 0.062 0.000 Constant -0.018* 0.001 0.000 33 Table 2.28: Persistence and Average Inflation: QTD, with xu Non-OECD Countries, N=29 Coeff. Std. Error p-value 0.917* 0.029 0.000 $11 -0.603* 0.170 0.000 0.027* 0.008 0.001 tt* -0.032* 0.010 0.002 Constant -0.004* 0.001 0.011 Table 2.29: Persistence and Average Inflation: HP, with xt, Non-OECD Countries, N=29 Coeff. Std. Error p-value 0.798* 0.033 0.000 $ i i -0.343 0.183 0.061 tt0 0.012* 0.007 0.104 tt* -0.019* 0.010 0.056 Constant -0.001 0.001 0.320 The exclusion of these episodes renders the coefficients statistically insignificant at any reasonable level of significance (see Table 2.30 and 2.31). In Tables 2.32 and 2.33 I report the results when Argentina, Brazil, and Israel are excluded from the estimation altogether. I find that the coefficients are not only statistically insignificant but also of the opposite sign from what is predicted by the theoretical model. In Tables 2.34 - 2.36 I present the results for the AR(2) dynamics in the Non-OECD countries. For Table 2.34 the x2 test statistic value is 12.1 and the p-value is 0.002 indicating that the null hypothesis is rejected. When I exclude the episodes of hyperinflation the x2 Table 2.30: Persistence and Average Inflation: QTD, with xt, Non-OECD Countries, Ex-cluding Episodes of Hyperinflation Coeff. Std. Error p-value 0.863* 0.033 0.000 $11 -0.192 0.402 0.528 tt0 0.096* 0.013 0.000 tt* -0.270* 0.004 0.002 Constant -0.009* 0.001 0.000 34 Table 2.31: Persistence and Average Inflation: HP, with xt, Non-OECD Countries, Ex-cluding Episodes of Hyperinflation Coeff. Std. Error p-value 0.749* 0.033 0.000 0.054 0.258 0.834 tt0 0.075* 0.012 0.000 tt* -0.243* 0.039 0.000 Constant -0.006 0.001 0.000 Table 2.32: Persistence and Average Inflation: QTD, with xt, Non-OECD Countries, Ex-cluding Argentina, Brazil, and Israel Coeff. Std. Error p-value 0.842* 0.034 0.000 0.019 0.936 0.528 tt0 0.146* 0.015 0.000 tt* -0.491* 0.055 0.002 Constant -0.012* 0.001 0.000 Table 2.33: Persistence and Average Inflation: HP, with xt, Non-OECD Countries, Ex-cluding Argentina, Brazil, and Israel Coeff. Std. Error p-value 0.751* 0.040 0.000 0.109 0.286 0.701 tt0 0.112* 0.014 0.000 tt* -0.406* 0.049 0.000 Constant -0.008 0.001 0.000 Table 2.34: Persistence and Average Inflation: AR(2), HP, with xt, Non-OECD Countries, N=29 Coeff. Std. Error p-value 1.132* 0.044 0.000 -0.723 0.211 0.001 -0.419* 0.044 0.000 ^* 0.453 0.211 0.032 tt0 0.011* 0.007 0.117 tt* -0.017* 0.009 0.073 Constant -0.001 0.001 0.310 35 Table 2.35: Persistence and Average Inflation: AR(2), HP, with xt, Non-OECD Countries Excluding Episodes of Hyperinflation Coeff. Std. Error p-value 1.053* 0.055 0.000 -0.298 0.356 0.403 -0.392* 0.055 0.000 $^i 0.491 0.361 0.174 0.064* 0.012 0.117 ty, -0.206* 0.038 0.073 Constant -0.005 0.001 0.000 Table 2.36: Persistence and Average Inflation: AR(2), HP, with xu Non-OECD Countries Excluding Argentina, Brazil, and Israel Coeff. Std. Error p-value 1.011* 0.058 0.000 $11 0.163 0.419 0.391 -0.338* 0.058 0.000 -0.019 0.423 0.964 0.095* 0.013 0.000 ty, -0.339* 0.048 0.073 Constant -0.007 0.001 0.000 36 test statistic value is 1.88 and the p-value is 0.391. This insignificance indicates that the null hypothesis cannot be rejected. That is, within the Non-OECD countries average inflation does not influence second-order output dynamics. Finally, for Table 2.36 the X2 test statistic value is 0.29 and the p-value is 0.866. The results for QTD case are qualitatively similar to the HP case and are not reported here. 2.6 The Two Stage Estimation In this section I follow a two stage estimation procedure similar to the one employed extensively in previous research that has focused on the influence of average inflation on the impact effects of aggregate demand shocks. In the first stage, I estimate country specific measures of persistence in output fluctuations. In the second stage of estimation, I examine how average inflation affects the estimated measures of persistence in the cross-section of countries. This approach is intuitively appealing as far as testing the cross-sectional implication of the theory is concerned, however, it assumes that countries are at different levels of steady inflation. Under this assumption, average inflation is the appropriate measure of the inflationary environment. As mentioned in the previous section, this assumption does not hold up in the data, in particular, for countries that have experienced episodes of hyperinflation. 2.6.1 A R ( 1 ) Specification In Stage 1, I estimate an AR(1) model of the detrended output and identify the coefficient on the lagged output deviation, /?,;, as the measure of persistence in country i UitD = Pi.yit-iD + axit + uiu (2.21) where y^D is the detrended output and xu is the nominal output growth of country i. In Stage 2, I estimate the following regression pt = S0 + Siiri + <527f,:2 + ei, (2.22) 37 Table 2.37: Persistence and Average Inflation: HP, N=51 Coeff. Std. Error p-value Si -0.566* 0.272 0.043 So 0.750* 0.036 0.000 Table 2.38: Persistence and Average Inflation: QTD, N=51 Coeff. Std. Error p-value Si -0.920* 0.252 0.001 So 0.870* 0.035 0.000 where 7r,; is the average inflation in country i. I use squared average inflation as a regressor to capture any non-linearities in the empirical relationship between persistence and average inflation. The results are reported in Tables 2.37 and 2.38 for the HP and QTD cases respectively. For the results reported in these tables I restrict 62 = 0. The standard errors reported in the tables are heteroscedasticity consistent. I find that the relationship between average inflation and persistence in the full sample is negative and significant for both QTD and HP filtered data. This finding is similar to the evidence reported in Kiley (1998). He interprets these results as strongly supportive of the sticky price models in explaining the observed persistence in output fluctuations. On the contrary, I argue that there are compelling reasons to question this evidence as supportive of the nominal rigidity models. I discuss the reasons in the following sections. Table 2.39: Persistence and Average Inflation: The Inverted-U Relationship, HP, N=51 Coeff. Std. Error p-value Si 1.005* 0.251 0.000 62 -1.921 0.205 0.000 So 0.617* 0.031 0.000 38 Table 2.40: Persistence and Average Inflation: The Inverted-U Relationship, QTD, N=51 Coeff. Std. Error p-value Si 0.723* 0.230 0.003 s2 -2.000* 0.225 0.000 So 0.727* 0.031 0.000 2.6.2 The Inver ted-U Relat ionship I find that there is a statistically significant inverted-U relationship between persistence and average inflation in the data. This relationship is at variance with a clear theoretical prediction of the sticky price models in which the frequency of price adjustment depends on the average inflation rate. From the results in Tables 2.39 and 2.40 I find the that the critical average inflation rate is 27% for HP filtered data and 18% for the QTD data. Below these critical average inflation rates, the relationship between persistence and average inflation is positive. In the entire sample only 5 countries are above the 27% average inflation and only 10 countries have average inflation rates above 18%14. 2.6.3 Episodes of Hyper inf la t ion The discussion in Section 2.4.1 made a case for excluding periods of extreme time variation in inflation for certain countries. Tables 2.41 and 2.42 provide the results for the case when episodes of hyperinflation are excluded. These results are once again striking. None of the measures of persistence have a statistically significant relationship with average inflation at the 5% level of significance. This implies that only episodes of hyperinflation are informative about the prediction of the theory. Finally, in Tables 2.43 and 2.44 I present the results for the case where the three coun-tries that experienced episodes of hyperinflation, namely, Argentina, Brazil, and Israel, are excluded in the estimation. The relationship between average inflation and persistence is 1 4Similar results hold when I restrict attention to the countries in the Ball, Mankiw, and Romer (1988) dataset. I find that the results are qualitatively similar when I use unanticipated nominal output growth to capture the impact effects of aggregate demand. I also controlled for supply shocks using the Producer Price Index for crude fuel and found similar results. 39 Table 2.41: Persistence and Average Inflation: Excluding Episodes of Hyperinflation, HP, N=51 Coeff. Std. Error p-value Si -0.189 0.385 0.624 So 0.690* 0.036 0.000 Table 2.42: Persistence and Average Inflation: Excluding Episodes of Hyperinflation, QTD, N=51 Coeff. Std. Error p-value Si -0.765 0.412 0.070 So 0.831* 0.037 0.000 found to be positive and statistically significant in HP filtered data( see Figures 2.4, 2.5, and 2.6). Also the inverted-U relationship is no relationship is no longer statistically significant (see Tables 2.45 and 2.46). The coefficients <Si and 62 are both jointly insignificant. 2.6.4 Alternative Measures of Persistence In Stage 1 I estimate an AR(1) specification VitD = PiVit-iD +Uit (2.23) to obtain the cumulative response of output deviations to aggregate demand shocks. This is given as: 1 As above, the prediction of the theoretical models is that the cumulative response of output fluctuations in high trend inflation countries should be smaller. I also estimate an AR(2) Table 2.43: Persistence and Average Inflation: Excluding Argentina, Brazil, and Israel, HP, N=51 Coeff. Std. Error p-value Si 0.340* 0.160 0.0.039 So 0.654* 0.027 0.000 40 1 Figure 2.4: Full Sample 41 D- O o •2 H .6 .2 .4 Average I n f l a t i on Figure 2.5: Excluding Episodes of Hyperinflation 42 Average Inflation Figure 2.6: Excluding Argentina, Brazil, and Israel 43 Table 2.44: Persistence and Average Inflation: Excluding Argentina, Brazil, and Israel, QTD, N=51 Coeff. Std. Error p-value Si 0.032 0.255 0.901 So 0.771* 0.032 0.000 Table 2.45: The Inverted-U Relationship: Excluding Episodes of Hyperinflation, HP, N=51 Coeff. Std. Error p-value Si -0.420 0.822 0.612 s2 0.564 1.145 0.701 So 0.705* 0.057 0.000 model of the detrended output to capture more general dynamics in the detrended output. Vt = PnVit-i + + eit-The cumulative response of output to aggregate demand shocks is given as 1 1 - A ; i - A ; 2 ' In Stage 2, I use these measures as dependent variables in 2.22 above. The results for these alternative measures of persistence are given in Table 2.47. They clearly indicate no relationship between average inflation and the cumulative response of output to aggregate demand shocks15. 1 5 I also checked the relationship between the unconditional variance of the AR(1) and AR(2) specifications and average inflation rate I VARW{y?) = T4p2=B{l3)o-l |/3|<1. Here, B((3), captures the extent to which the variability of output fluctuations is magnified by the persistence Table 2.46: The Inverted-U Relationship: Excluding Episodes of Hyperinflation, QTD, N=51 Coeff. Std. Error p-value Si 0.079 0.940 0.933 s2 -2.066 1.719 0.235 So 0.778* 0.063 0.000 44 Table 2.47: Alternative Measures: Full Sample, HP Persistence Measure Si <5o 1 1-/3 1.033 (8.69) 6.561* (1.39) l i-A-ft> -1.758 (1.52) 3.768* (0.32) S.E. in brackets. * = Sig. at 5% level. N = 51 Table 2.48: With Country Specific Characteristics: Dependent Variable = /3, QTD Variable Full Sample Excl. Hyp. Inf Epi. Excl. A, B, I TT -0.671* (0.24) -0.362 (0.44) -0.207 (0.35) OPEN™ 0.0006 (0.0003) 0.0008* (0.0004) 0.0006 (0.0003) OECDUM 0.02 (0.07) 0.147 (0.11) -0.003 (0.07) LATINDUM 0.170* (0.06) 0.155* (0.06) 0.129* (0.05) PCY70 -0.56E-5 (0.1E-4) -0.17E-4 (0.15E-4) 0.1E-5 (0.9E-5) So 0.775* (0.08) 0.722* (0.10) 0.702* (0.09) S.E. in brackets. * = Sig. at 5% level. N=51 N=51 N=48 2.6.5 Other Country-Specif ic Characterist ics I allow for per-capita income differences PCY-JO across countries, trade-openness of coun-tries (OPEN), persistence in the exogenous driving process px as measured by the auto-correlation in nominal output growth, and a dummy for Latin American countries. The consideration of these country specific characteristics does not alter the conclusions parameter. B(P\,Pz) is obtained from the unconditional variance of the AR(2) model which is given as The conditions for covariance stationarity \p2\ < 1, -2 < ft < 2, ft + p2 < 1, P2 - Pi < 1 are satisfied for all countries. None of these results are statistically significant. Similar results hold for QTD data. 45 Table 2.49: With Country Specific Characteristics: Dependent Variable = 3, QTD Variable Full Sample Excl. A, B, I 7T -0.717* (0.23) -0.309 (0.37) Px 0.192* (0.09) 0.154 (0.09) OPENro 0.0005 (0.0003) 0.0006 (0.0003) OECDUM 0.0001 (0.07) -0.024 (0.06) LATINDUM 0.162* (0.05) 0.123* (0.05) PCY70 -0.7E-5 (0.9E-5) 0.3E-6 (0.8E-5) So 0.704* (0.09) 0.655* (0.10) S.E. in brackets. * = Sig. at 5% level. N=51 N=48 in any manner (see Tables 2.48 and 2.49)16. 2.7 Concluding Remarks In this chapter I investigated a key implication of the sticky price model of business cycle that is designed to explain the observed persistence in output fluctuations around its log-run growth path. A prediction of this model is that higher trend inflation rate will increase the frequency of price adjustment and thereby inversely affect the persistence in deviations of output from its trend. Therefore, countries with high trend inflation rate should have less persistent output fluctuations. The characteristics of the dataset available to examine this hypothesis raises several implementation issues. I pay particular attention to these issues in a manner that is consistent with the theoretical framework of the model. My estimation results, in general, do not support the hypothesis that higher inflation countries have less persistent output fluctuations. In a particular case, I find extremely fragile support for the hypothesis. This support is found to be driven by a few episodes of hyperinflation. The lack of support for the hypothesis raises a problem for the propagation mechanism based on sticky prices. If price stickiness is indeed the central mechanism for the trans-mission of monetary shocks to the real side of the economy in a persistent manner then 1 6 The variables PCY70 and OPEN = I ^ i E £ I g ± | 2 L E £ I l £ w e r e obtained from the Penn World Tables. Similar-results hold for HP filtered data. 46 one has to assume that the costs of nominal contracting are inelastic with respect to the inflationary environment over a very broad range of inflation - from 2% - 3% to 60% -70%. However, such a position is intuitively unappealing. Therefore, the results of this paper suggest that further investigation of the sticky price channel is required before it can provide a solid microfoundation for explaining persistence of output fluctuations. 47 Data Summary Data Summary No. Country Period Avg. Inflation (% 1 Argentina 66-81 97.7 2 Australia* 52-96 6.1 3 Austria* 67-95 4.7 4 Belgium* 56-94 4.4 5 Bolivia 61-83 31.1 6 Brazil 66-84 58.4 7 Canada* 51-96 4.4 8 Colombia 71-96 23.1 9 Costa Rica 63-96 16.6 10 Denmark 53-96 5.6 11 Dominican Republic 66-96 13.5 12 Ecuador 68-96 25.7 13 El Salvador 54-96 7.3 14 Finland 63-96 7.3 15 France* 53-96 5.7 16 Germany* 53-86 3.6 17 Greece* 51-94 11.4 18 Guatemala 54-96 8 19 Iceland* 63-96 23.9 20 India 61-95 8.1 21 Iran 67-96 18.9 22 Ireland* 51-96 6.8 23 Israel 71-96 65.2 24 Italy* 63-96 9.6 25 Jamaica 63-94 17.5 26 Japan* 59-96 4.8 27 Kenya 68-96 10 28 Malaysia 71-96 4.8 29 Mexico 51-85 16.9 30 Netherlands* 59-96 4.5 31 New Zealand* 55-96 7.1 32 Nicaragua 63-83 9.8 33 Norway* 52-96 5.4 34 Pakistan 54-96 7.8 35 Panama 53-96 2.6 36 Paraguay 60-96 14.3 37 Peru 63-84 35.2 38 Philippines 51-96 8.7 39 Portugal* 69-96 14.4 40 Singapore 63-96 3.6 41 South Africa 51-96 8.8 42 South Korea 54-96 15.1 43 Spain* 57-96 9.5 44 Sweden* 53-95 6 45 Switzerland" 51-96 3.6 46 Thailand 51-96 4.9 47 Tunisia 71-96 7.3 48 UK* 51-96 6.7 49 US- 51-96 4.3 50 Venezuela 60-96 19 51 Zaire 53-84 26.4 ' indicates OECD country (22 countries). Mexico and S. Korea became OECD members in 1994 and 1996 respectively. 48 Chapter 3 Price Stickiness, Inflation, and Real Exchange Rate Dynamics: A Cross-Country Analysis An important puzzle in international macroeconomics is why real exchange rates exhibit, persistent deviations from purchasing power parity (PPP)1. Froot and Rogoff (1995, Pg. 1648) summarize the time series evidence as: Consensus estimates put the half-life of deviations from PPP at about 4 years for [real] exchange rates among major industrialized countries. One explanation for this phenomenon which has received considerable attention is based on sticky prices2. Monetary shocks may cause a change in the nominal exchange rate. In the presence of sticky prices the national price levels are either fixed or very slow to adjust 3 . Therefore, the real exchange rate ( nominal exchange rate adjusted for differences in national price levels) would deviate from PPP. The duration of such deviations from PPP depends directly on the time it takes for prices to adjust fully. A prediction of the sticky price model of real exchange rate fluctuations is that: The deviations of real, exchange rates from, PPP should be less persistent in countries with high trend inflation relative to countries with low trend inflation. The idea is fairly intuitive. Prices adjust faster in high inflationary environments relative to the low ones4. This rapid ^ee, for example, Rogoff (1996). 2 The existence of sticky prices has been rationalized by assuming fixed costs of price adjustment some-times referred to as "menu-costs". This approach is due to Mankiw (1985) and Akerlof and Yellen (1985). 3Examples of papers that have emphasized the sticky price framework for real exchange rate fluctuations are Ohanian, Stockman, and Killian (1985), Svensson and Wijnbergen (1989), Obstfeld and Rogoff (1995, 1996), and Kollmann (1997). The slow adjustment of the national price level is attributed to staggering of sticky pricing decisions among firms as studied in pioneering papers by Taylor (1980) and Blanchard (1993). 4 The dependence of price stickiness on the inflationary environment is formalized by Romer (1990) in a static setting. More recently, Dotsey, King, and Wolman (1998) examine the influence of the inflationary environment on the frequency of price adjustment in a dynamic framework. 49 adjustment will reduce the stickiness in the national price level. As a result, monetary-shocks would be absorbed into the price level faster. Since the degree of price stickiness determines the persistence of the monetary shocks on the economy, lower price stickiness in high inflation countries implies that the deviations of real exchange rate from PPP in these countries should be less persistent. The objective of this paper is to examine this prediction of sticky price models of real exchange rate fluctuations. At the theoretical level developing models that can replicate the observed persistence in real exchange rates has been a challenging task. Recent research effort has been towards developing general equilibrium models with sticky prices (with pricing decisions staggered across firms) and pricing-to-market (PTM) behaviour of firms5. The incorporation of PTM behaviour as an important building block in addition to sticky prices is motivated by the empirical work of Engel (1993) and Knetter (1993). For example, Engel (1993) finds that real exchange rate fluctuations are almost entirely associated with fluctuations in the relative price of identical traded goods. This observation can be captured by introducing price discriminating monopolists in the dynamic general equilibrium models. Betts and Devereux (1996, 1998), Kollmann (1997), Chang and Devereux (1998), Chari, Kehoe, and McGrattan (1998), Bergin and Feenstra (1999) are examples of such models of sticky prices and P T M 7 . The motivation behind staggering of pricing decisions is to generate inertia in the price level adjustment so as to enhance the persistent effect of monetary shocks. The seminal work of Taylor (1980) and Blanchard (1983) has demonstrated the importance of 5Under P T M a firm chooses to set different prices for its products across segmented markets6. Earlier par-tial equilibrium models in this vein were developed by Dornbusch (1987), Krugman(1987), Knetter(1989), and Marston (1990). 7Chari, Kehoe, and McGrattan (1998) find that prices have to be sticky for extended periods of time to match the observed persistence of real exchange rate deviations from PPP. However, Bergin and Feenstra (1999) show that enriching the structure of preferences (using translog preferences which generate non-$o elasticity of demand for products), P T M and staggered sticky prices provide an environment which can match the observed serial correlation in real exchange rate fluctuations. Bergin and Feenstra (1999) show that the introduction of non-$o elasticity gives rise to interactions in the price setting rules for firms which enhances persistence. They also argue that rationalizing P T M behaviour requires the presence of home-bias in consumption preferences. Chang and Devereux (1998) have clarified that P T M by itself cannot generate adequate persistence in real exchange rate fluctuations. The presence of price stickiness is a necessary condition. 50 this channel for the propagation of shocks. If price stickiness declines with an increase in trend inflation as in Romer (1990) and Dotsey, King, Wolman (1998), the inverse relationship between trend inflation and persis-tence in real exchange rate fluctuations is a prediction of this class of models. Given the importance of price stickiness as a microfoundation for explaining persistence in exchange rate fluctuations it is useful to investigate the present hypothesis. I use annual data from 49 countries over the period 1972 - 1996 to investigate the inverse relationship between the inflation and persistence in real exchange rate fluctuations. In the empirical implementation I pay careful attention to the issue of time variation in inflation within countries. I find a negative relationship between persistence in real exchange rate fluctuations and trend inflation, but further tests reveal that the support for this inverse relationship in the data is extremely fragile. The statistical significance of the inverse relationship is influenced drastically by only a few episodes of hyperinflation. I argue that for an accurate implementation of the hypothesis these episodes should be excluded from the empirical analysis. The exclusion of these episodes which constitute less than 3% of the entire data renders the relationship between inflation and persistence in real exchange rates statistically insignificant. These results are difficult to reconcile with the view that prices are less sticky in higher inflationary environments and therefore real exchange rate fluctuations should be less persistent. Based upon these results a number of issues arise about the sticky price framework as an explanation of the persistent nature of exchange rate fluctuations. I discuss these issues in detail below. The organization of the paper is as follows: In section 3.2, I describe the theoretical structure that underlies my empirical analysis. Section 3.3, I discuss the empirical imple-mentation issues and provide data information. In section 3.4, I present my results and discuss their implications. Section 3.5 concludes. 51 3.2 Theoretical Framework In section 2.2 I described the theoretical structure which captures the link between the price stickiness and trend inflation. A similar structure illustrates how sticky prices can lead to persistence in real exchange rate fluctuations and how the trend inflation impinges upon the degree of persistence. Consider two countries, home and foreign. Then, following Equation 2.2 and 2.7, the symmetric equilibrium aggregate price level for the home economy (Pt) and the foreign economy (Pf) can be written as Pt = [(1 - ^ X P / ) 1 - + ^ T ) ( P t - i ) 1 - ^ (3.1) and Pf = [(1 - * F ( 7 r J ) ) ( P ; * y - 6 ' + ^ ( T T ? ) ^ ) 1 - ' ' ] ^ , (3.2) where e and ep are the elasticities of demand in the home and foreign countries respec-tively. The expression for the equilibrium aggregate price level has two components. First, a fraction, 1 — 0, of firms charge the optimal price P* at time t. Second, the remaining fraction of firms, 0, charges the predetermined price Pt-\- Thus, the aggregate price level is completely characterized by {P*,Pt-\}. Also, the price level Pt contains prices of both domestic and imported goods. This is due to the assumption of P T M a foreign exporter can charge an exclusive price in the local currency (see Betts and Devereux (1998)). The inflation rate is given as irt = — 1. Correspondingly for the foreign country. The real exchange rate for a country (qt) is defined as Pt_ where et is the nominal exchange rate (units of foreign currency per unit of domestic Qt = et- F , 52 currency)8. In a DGE model with sticky prices (for example, Devereux and Engel (1999)) the nominal exchange rate, in equilibrium, is proportional to the changes in domestic (Mt) and foreign money(M*). That is, et oc By rewriting the definition of real exchange rate using (3.1) as lit = eit , (3.3) "it it is easy to see the implications of varying the degree of price rigidity as captured by <f>. If <f> = 0, then prices are completely flexible. If (j) = 1, then prices are completely rigid. A higher trend inflation would make </>(.) smaller and therefore increase the frequency of price adjustments among firms. A large fraction of the firms, 1 — (/)(•), in the economy adjust prices in response to monetary shocks. Consequently, the national price level absorbs the effect of shocks quickly. Therefore, real exchange rate fluctuations are less persistent. 3 . 3 E m p i r i c a l I m p l e m e n t a t i o n I postulate the following linear process for real exchange rates qit = ty(ct>{f(IIu)))qit-i+uit, (3.4) where (i denotes the country) i = 1,...,N and t = l , . . . ,Tj . qu denotes the HP-filtered real exchange rate for country i. The term 0(.) captures how the inflationary environment, f(Uit), influences the persistence of real exchange rate fluctuations as captured by the coefficient on the lagged real exchange rate. I discuss this interaction below. The error term un captures the shocks to the real exchange rate. I consider two representations of the inflationary environment f(Hit) for each country: J 7rJt : the long-run (trend) inflation rate, j(JA.it) = \ _" (3.5J 7T7; : the average inflation rate. 8In the empirical analysis I make U.S. dollar the "common foreign country" for every country, therefore, the nominal exchange rate is: US dollars per unit of currency i. 53 The advantage of considering the long-run trend inflation is that it explicitly takes into account the time variation in inflation over the sample period 9 . I discuss this aspect in detail below. I take the linear approximation of (3.4) to get the following specification 1 0 qlt = $ 0 + *i<7,;t-i + $7-/'(n ? ; t) * qit-i + uit. (3.6) The definition of persistence in real exchange rate that I consider in this section is: how closely is the deviation of real exchange rate from, its trend in the current period related to the deviation of real exchange rate from, its trend in the previous period. That is, ^ - = $ 1 + * T/(n i t). (3.7) I am interested in examining how the inflationary environment affects this persistence, that is, the cross-partial df(Uit)dqit-i Therefore, the coefficient 3?^  captures the interaction between the lagged real exchange rate and the inflationary environment is the parameter of central interest. The class of nominal rigidity models with staggered price setting among firms that have been used to explain the observed persistence in real exchange rate deviations imply that an increase in the trend inflation will make firms adjust their prices more frequently in response to aggregate demand (monetary) shocks. As a result, the national price level will change more rapidly and therefore real exchange rate fluctuation should be less persistent. The theoretical prediction of this class of models is that 3>n should be negative. I estimate the following specification for the panel countries allowing for cross-sectional heteroscedasticity. 9The long-run trend inflation component is extracted using the HP filter. I also considered the actual inflation rate (nu) which captures all the time variation. The results were qualitatively similar and therefore not reported here. 1 0Froot and Rogoff (1995) use the specification qu = fl.o + pqit-i +£u for a panel of countries and identify the parameter p as the persistence in the real exchange rate movements. 54 qu = $0 + *l<?it-l + *7r/(n) * qit-i + un. Denning /(II) * qu-\ = ^2,u I can write the above equation as (3.9) qi " 1 qi X2,l a U l * $i + qso _ l qso X2,50 $ 2 u 5 0 where q; = [qii---qiTj]', qj = [QiO---QiTi-iY> a n A u i = [ un---UiTiY The above can be compactly written as q = X $ + u. The covariance matrix is given as: £[uu'j = fl where fl = E N X N ^ I T J X T ! - The off-diagonal elements of the fl matrix are all zeros due to the unbalanced nature of the data1 1. I allow for cross-sectional heteroscedasticity thus Diag(T,) = [Si...£50]'- I conduct Feasible GLS estimation to obtain $ = ( X ' f H X ^ X ' f i - ^ q , (3.10) where E, ;, ; = H ^ . 3.3.1 D a t a I use annual IFS data on bilateral nominal exchange rates (en, US Dollars per unit of currency in country i), & real and nominal GDP ( or GNP ) to obtain the GDP deflator for 49 countries12. The overall sample period is 1972 - 1996 (see the Data Summary section at the end of this chapter). For each country I construct the real exchange rate (qu) series as P>* qu — eu pUS • 1 1 For Greece and Zaire the data are available for the periods 1972 - 1994 and 1972 - 1993 respectively. 1 2 The nominal exchange rate data is the IFS series rh which denotes US dollars per unit of national currency. 55 Table 3.1: Real Exchange Rate Persistence and Trend Inflation: Full Sample Coeff. Std. Error p-value 0.661* 0.025 0.000 $* -0.188* 0.079 0.018 $0 0.005* 0.002 0.008 Table 3.2: Real Exchange Rate Persistence and Average Inflation: Full Sample Coeff. Std. Error p-value 0.667* 0.027 0.000 3v -0.249* 0.107 0.021 $ 0 0.005* 0.002 0.008 where i y is the price index in the US and P*t is the price index in country i. I detrend the data using the HP filter13. The price index is the GDP ( or GNP ) deflator. I construct the inflation series as the growth rate of the price index. 3.4 Results In Tables 3.1 and 3.2 I present the results for the full sample14. The coefficient of interest on the interaction variable $ 1 : L is negative and statistically significant for both the trend and the average inflation. These empirical findings support the hypothesis that persis-tence in the deviations of real exchange rate should be inversely related to trend inflation. The results are consistent with the prediction of the sticky price model of exchange rate fluctuations in which price stickiness depends on trend inflation. I find that explicitly allowing for long-term time variation by using trend inflation and using average inflation gives similar results. One interpretation is that the hypothesis is 1 3 The underlying assumption is that the real exchange rate has a trend. This trend may arise due to the differences in productivity growth across traded and non-traded sector. Such differences may lead to a trend in the relative price of goods. These prices are included in the measure of real exchange rate. That real exchange rates exhibit trend stationaiity implies a failure of long-run absolute PPP but not relative PPP (see Froot and Rogoff (1995) for a discussion of this point). The results for quadratic time detrended real exchange rates are qualitatively similar to the HP filter results. 1 4 In all the Tables '*' indicates that the coefficient is statistically different from zero at the 5% level of significance. The p-value shows that the exact significance level below which the null hypothesis for the parameter of interest(In the present case, Ho : ^ J 1 = 0) cannot be rejected. 56 supported in by the data. An alternative interpretation, which I emphasize, is that for the sample period under consideration the influence of time variation is only partially captured by the trend inflation. The coefficient on the interaction term when I use trend inflation (which takes into account the long term movements in inflation) is smaller than the coefficient on average inflation15. In this situation it becomes even more crucial to identify a relatively stable period of inflation within countries for the empirical analysis. In the next section I highlight the importance of this issue. 3.4.1 Episodes of Hyper inf la t ion In Section 2.4.1 I discussed the ideal environment for testing the hypothesis in a cross-country analysis especially when one is considering how the inflationary environment may influence persistence. Therefore, to conduct the analysis in a manner that is closer to the assumptions behind the theoretical prediction I reduce the time variation in inflation within countries by excluding the episodes of hyperinflation. This strategy yields a relatively stable cross-section of inflationary environments. Towards this end, and as in Chapter 1, I identify periods of relatively stable inflation within the high inflation countries by examining the volatility of inflation in sub-sample periods (see Table 3.3). The last column in Table 3.3 contains the relative inflation volatility across the periods. The unstable period in Argentina is more than three times as volatile as the stable period. In Brazil and Israel the volatility of the unstable period is about five times that of the stable period. The years that constitute relatively high inflation volatility are episodes of hyperinflation. In the hyperinflationary periods the inflation rate was greater than three standard deviations of the average inflation for the non-hyperinflationary period (see Figures 3.1, 3.2, 3.3)16. The episodes of hyperinflation in Argentina, Brazil, and Israel constitute less than 3% of the entire panel data. In Tables 3.4 and 3.5 I present the results for the case where the episodes of hyperinfla-1 5 When I use the actual inflation rate the coefficient of interest is half the coefficient than when average inflation is used. 1 6 The horizontal dotted line is nst.abie + 3 * 0Ti„tabu- The time and cross-section dimensions of the panel have a total of 1147 observations. 57 3.5 A R G E N T I N A : 1 9 7 3 - 1996 Actual and Trend Inflation Figure 3.1: Argentina: Actual (dark line) and Trend Inflation Rates (1973-1996) Table 3.3: Episodes of Hyperinflation Country Period Years TT an Relative Volatility Argentina Full Sample 1973-1996 1.052 0.9048 1.76 Unstable 1989-1994 1.52 1.63 3.18 Stable 1973-1988 1.101 0.5122 1 Brazil Full Sample 1973-1996 1.185 1.0113 4.76 Unstable 1984-1996 1.784 1.0366 4.88 Stable 1973-1988 0.477 0.2121 1 Israel Full Sample 1973-1996 0.421 0.4219 4.90 Unstable 1973-1985 0.637 0.4743 5.15 Stable 1986-1996 0.167 0.0860 1 58 BRAZIL : 1973 - 1996 Actual and Trend Inflation igure 3.2: Brazil: Actual (dark line) and Trend Inflation Rates (1973-1996) 59 I S R A E L : 1973 - 1996 Actual and Trend Inflation 60 Table 3.4: Real Exchange Rate Persistence and Trend Inflation: Excluding Episodes of Hyperinflation Coeff. Std. Error p-value 0.657* 0.027 0.000 $* -0.126 0.100 0.210 $0 0.006* 0.002 0.004 Table 3.5: Real Exchange Rate Persistence and Average Inflation: Excluding Episodes of Hyperinflation Coeff. Std. Error p-value 0.655* 0.028 0.000 -0.129 0.129 0.327 $0 0.006* 0.002 0.004 tion are excluded. In contrast to the results for the full sample case, the results in Tables 3.4 and 3.5 are striking. The exclusion of a few episodes of hyperinflation eliminates the statistical significance of the inverse relationship between persistence in real exchange rates and trend (and average) inflation. The statistical insignificance of the inverse relationship carries over to the case where I exclude Argentina, Brazil, and Israel altogether. The results for this case are reported in Tables 3.6 and 3.7. These results have important implications for the sticky price framework for explaining the observed persistent deviations of real exchange rate from PPP. First, the results suggest that persistence in real exchange rate fluctuations is influenced by trend inflation only in periods of extremely high inflation. If price stickiness is indeed the central mechanism for the transmission of monetary shocks into real exchange rates then the results suggest that price stickiness is not influenced by inflation in any quantitatively significant manner unless one takes into account periods of extreme monetary instability. However, such a position is intuitively unappealing since it is difficult to imagine that the duration for which prices are kept fixed in a low inflation country such as Canada is the same as it is in Argentina. In other words, one has to assume that the costs of nominal contracting are inelastic with respect to the inflationary environment over a very broad 61 Table 3.6: Real Exchange Rate Persistence and Trend Inflation: Excluding Argentina, Brazil, and Israel Coeff. Std. Error p-value 0.660* 0.027 0.000 -0.131 0.120 0.274 $0 0.006* 0.002 0.007 Table 3.7: Real Exchange Rate Persistence and Average Inflation: Excluding Argentina, Brazil, and Israel Coeff. Std. Error p-value 0.659* 0.032 0.000 -0.137 0.190 0.470 0.006* 0.002 0.007 range of inflation - from 2 - 3% to 80 - 90%. Second, the results indicate that one can learn about the prediction of sticky price models for persistence in real exchange only from episodes of hyper inflation which are essentially periods of enormous turbulence and monetary instability in the economy. How-ever, most macroeconomic models are constructed for stable stationary environments. 3.4.2 O E C D and N o n - O E C D Countries In this section I divide the sample into OECD and Non-OECD countries to examine the prediction of the sticky price models of real exchange rate persistence across two prominent country blocks. In the sample there are 21 OECD and 29 Non-OECD countries. The average inflation within the OECD countries varies from 3.5% to 24.82%. Hence, there is sufficient cross-sectional variation within this group of countries. For the Non-OECD countries the average inflation varies from 4% to 123%. In Tables 3.8 and 3.9 I present the results for the OECD countries. The coefficient of interest, is not statistically significant. This finding shows that within the OECD countries there is no relationship between persistence in the deviations of real exchange rates from PPP and trend inflation. A similar result holds for the relationship between 62 Table 3.8: Real Exchange Rate Persistence and Trend Inflation: OECD Countries Coeff. Std. Error p-value 0.628* 0.053 0.000 0.369 0.517 0.476 $0 0.005 0.003 0.117 Table 3.9: Real Exchange Rate Persistence and Average Inflation: OECD Countries Coeff. Std. Error p-value $1 0.645* 0.061 0.000 0.167 0.635 0.793 $0 0.005 0.003 0.179 persistence and average inflation. For the Non-OECD countries I find that the hypothesis is strongly supported. The coefficients in all the both cases are negative and statistically significant (see Tables 3.10 and 3.11). These results are similar to the full sample case (Tables 3.1 and 3.2). They once again indicate that one can learn about the hypothesis only from periods of extreme monetary instability. This point is clearly illustrated when I exclude the episodes of hyperinflation in the three Non-OECD countries, namely, Argentina, Brazil, and Israel. I report the results in Tables 3.12 and 3.13 for the trend and the average inflation cases respectively. The results in Table 3.12 show that even within the Non-OECD countries, the hypoth-esis of an inverse relationship between real exchange rate persistence and trend inflation is not supported. The extreme observations that contribute to enormous time-variation contain all the information as far as the support for the hypothesis is concerned. Table 3.10: Real Exchange Rate Persistence and Trend Inflation: Non-OECD Countries Coeff. Std. Error p-value 0.649* 0.037 0.000 -0.187* 0.084 0.027 $0 0.006* 0.002 0.023 63 Table 3.11: Real Exchange Rate Persistence and Average Inflation: Non-OECD Countries Coeff. Std. Error p-value 0.654* 0.039 0.000 tt* -0.240* 0.116 0.038 $0 0.006* 0.002 0.023 Table 3.12: Real Exchange Rate Persistence and Trend Inflation: Non-OECD Countries, Excluding Episodes of Hyperinflation Coeff. Std. Error p-value ttl 0.646* 0.038 0.000 tt* -0.128 0.108 0.235 ttfj 0.006* 0.002 0.012 Table 3.13: Real Exchange Rate Persistence and Average Inflation: Non-OECD Countries, Excluding Episodes of Hyperinflation Coeff. Std. Error p-value ttl 0.639 0.041 0.000 tt* -0.110* 0.141 0.434 <f>0 0.006* 0.002 0.023 64 3.4.3 Two-S tage E s t i m a t i o n In this section I use the Two-Stage Approach to examining the prediction of macroeconomic models. Lucas (1973) and Ball, Mankiw, and Romer (1988) are two prominent examples of this strategy. In the first stage I run a country specific regression to estimate the parameter Pi which captures the persistence in real exchange rates. <lit = PiQit-i + uit. (3-11) In the second stage I regress the estimated coefficients p^s on average inflation rates. ft = A) + / ? i * ^ + « i , i = l,...,50. (3.12) I present the results in Table 3.1417. The results from this alternative estimation method-ology are qualitatively very similar to the panel data results from the previous section. In the full sample the coefficient fi\ is negative and statistically significant. As found in earlier results, the episodes of hyperinflation have a drastic influence. Once these episodes are excluded I find that there is no relationship between persistence in real exchange rate fluctuations and average inflation. Further, within the OECD countries there is no support for the hypothesis. For the Non-OECD countries the coefficient is negative and statistically significant. However, the exclusion of episodes of hyperinflation leads to the conclusion that there is no relationship between persistence in real exchange rate fluctuations and average inflation. Therefore, using this alternative approach I find that the results are similar to the panel data results of the previous section. 3.4.4 Vo la t i l i t y O f R e a l Exchange Rates and A v e r a g e Inf lat ion An important stylized fact about the real exchange rate fluctuations is that they are ex-tremely volatile. This behaviour has been documented by Mussa (1986) and many others. Sticky price models of exchange rate fluctuations predict that the volatility of real exchange rates should be inversely related to the trend inflation level. Chadha (1987) shows that the 1 7 The standard errors are heteroscedasticity-consistent. 65 Table 3.14: Two-Stage Estimation: Dependent variable is pi Countries Pi 00 Full Sample -0.220* (0.09) 0.541* (0.02) Full Sample (Excl. Episodes) 0.063 (0.11) 0.520* (0.02) Excluding A, B, I 0.030 (0.17) 0.520* (0.02) OECD 0.221 (0.50) 0.485* (0.03) Non-OECD -0.305* (0.09) 0.573* (0.03) Non-OECD (Excl. Episodes) 0.175 (0.13) 0.577* (0.03) longer the length of price contracts (a form of nominal price stickiness), the greater is the volatility of real exchange rate18. In Section 2.2, I showed that the average duration of price contract is given by and that this measure of price stickiness is inversely related to trend inflation. A prediction of this model is that in high inflation countries, the shorter-length of nominal contracts due to high trend inflation should lead to less volatile real exchange rates. I estimated the following regression to test this prediction: o-qi = So + r5i7fj + Vi, (3.13) where aq. is the volatility of the HP filtered real exchange rates. The prediction of the sticky price model is that b\ should be negative. The estimation result from the above regression does not support the prediction (see Table 3.15). The coefficient of interest, <5i, is positive and statistically insignificant. 1 8Chadha (1987) shows that an increase in the growth rate of money supply or an increase in the variability of innovation in the money supply lead to a decrease in the average contract length. These conditions are likely to hold in high inflation countries. The results of Chadha (1987) are similar to the results obtained by Gray (1978), Canzoneri (1980), and Kandil and Gray (1993). 66 Table 3 . 1 5 : Volatility of Real Exchange Rates and Average Inflation Si <5o Full Sample 0 . 0 0 5 ( 0 . 0 9 ) 1.166 ( 0 . 8 0 ) 3.5 Discussion The empirical results of this chapter further reinforce the conclusions drawn from the analysis in chapter 2. The results show that if price stickiness is indeed endogenous, that is, the degree of price stickiness depends inversely on the trend inflation of the economy, then, a key prediction of the sticky price model is not supported by the data. The persistence in real exchange rate fluctuations is, in general, not influenced by trend inflation. The prediction is supported only when one takes into account periods of extreme monetary phenomena. In this case, it is likely that the inverse relationship arises due to some reason other than high frequency of price changes. For instance, the autocorrelation in the HP filtered real exchange rate for Israel is negative ( - 0 . 0 9 ) . If price stickiness were to completely disappear at very high levels of inflation then the sticky price model predicts that this autocorrelation should be zero and not negative. A natural step at this stage is to examine other potential candidate explanations and difficulties associated with each. 3.5.1 Market Incompleteness In the presence of incomplete markets, monetary shocks may cause permanent wealth redistribution. This wealth redistribution may lead to persistent real exchange rate move-ments. It has not been explored whether price stickiness is a necessary condition even in this environment. 3.5.2 Distortionary Taxation Alesina and Perotti ( 1 9 9 5 ) show that government spending when financed by distortionary taxes can have long-run effects on the relative price of nontradables. This channel can 67 potentially cause persistent movements in real exchange rates. However, only a small fraction of the variability in real exchange rates is attributed to the relative prices of nontradables as shown by Engel (1995). 3 . 5 . 3 Strategic Price Competition A large body of literature in industrial organization shows that nominal prices may be sticky at the micro level due to collusive concerns in the presence of strategic competition among firms. It would be useful to explore the consequences of this form of price stickiness to explain persistence in real exchange rate fluctuations. In particular, one needs to examine what influence a high trend inflation may have on strategic competition. I plan to explore these issues in future work. 3 . 5 . 4 Non-monetary shocks An alternative to sticky price framework is one in which prices are completely flexible and real exchange rates are driven by real shocks, for example, productivity shocks. An example of this alternative view is presented in Stockman (1988)19. However, under this view monetary policy innovations are completely neutral. This result is at variance with the evidence of Clarida and Gali (1994) and Eichenbaum and Evans (1995) who find a strong link between monetary policy and exchange rates. 3 . 6 C o n c l u s i o n In high inflationary environments prices adjust more frequently. Firms experience rapid changes in their relative prices and, therefore, nominal inertia due to menu costs should be less important. Therefore, a sticky price model of real exchange rate fluctuations implies that the trend inflation level must inversely affect the persistence in the deviations of real exchange rate from PPP. That is, countries with high trend inflation should have less persistent real exchange rate fluctuations. In this paper I investigated this hypothesis for 19See, for example, Backus, Kehoe, and Kydland (1995) for a dynamic general equilibrium approch to international business cycles. 68 a panel of countries. The results reveal that the support for this hypothesis is extremely fragile. The support for the hypothesis is found only when extreme monetary phenomena - such as hyperinflations - is taken into account. It is likely that in this particular case the inverse relationship is driven by forces other than sticky prices. In general, the persistent nature of real exchange rate fluctuations is not influenced by trend inflation rate. The results are difficult to reconcile with the sticky price model that is used to explain the persistent nature of real exchange rate fluctuations. I conclude that further research on the interaction of inflation with the structural features of the economy such as strategic competition and market incompleteness could prove fruitful in shedding more light on this issue. 69 Data Summary Data Summary No. Country Avg. Inflation (%) 1 Argentina 100.1 2 Australia* 7.5 3 Austria* 4.4 4 Belgium* 5 5 Bolivia 6 6 Brazil 123 7 Canada* 5.5 8 Colombia 21.7 9 Costa Rica 19.3 10 Denmark 6.3 11 Dominican Republic 15.1 12 Ecuador 25.4 13 El Salvador 12.3 14 Finland 7.4 15 France* 6.6 16 Germany* 3.6 17 Greece* 16.8 18 Guatemala 12.9 19 Iceland* 24.8 20 India 8.5 21 Iran 20.3 22 Ireland* 8.1 23 Israel 43.5 24 Italy* 10.9 25 Jamaica 20.6 26 Japan* 3.7 27 Kenya 10.9 28 Malaysia 4.9 29 Mexico 29.3 30 Netherlands* 3.8 31 New Zealand" 8.7 32 Norway" 6.34 33 Pakistan 9.8 34 Panama 4 35 Paraguay 17.5 36 Philippines 11.9 37 Portugal* 15.3 38 Singapore 4.1 39 South Africa 12.9 40 South Korea 11.1 41 Spain* 10.4 42 Sweden* 7.4 43 Switzerland* 3.5 44 Thailand 6.4 45 Tunisia 7.3 46 UK* 8.3 47 US* 5.4 48 Venezuela 20.8 49 Zaire 78.7 ' indicates OECD country (22 countries). Mexico and S. Korea became OECD members in 1994 and 1996 respectively. 70 Chapter 4 Product Diffusion, Increasing Returns to Specialization, and the Propagation of Shocks The objective of this paper is to explore the role of diffusion of new products in prop-agating technology shocks. I make two main assumptions. First, the more products there are, the better it is for the economy. That is, once products get diffused in the economy, they enhance the productivity of factors such as labour and capital. In the literature this phenomenon is referred to as increasing returns to specialization.1 Second, the diffusion of new products in the economy takes time. New products may arise not only in the product space but also in geographic, and/or information spaces. Therefore, it will be useful to interpret the term 'new products' broadly as innovations. For example, a firm that introduces a new computer program for managing customer information may rapidly increase the productivity in other firms which adopt that program. Similarly, availability of new products in the geographical space may save resources spent on transportation and transaction costs for all firms. Finally, one could also think of the contribution that new products make in generating information about market conditions. Such information could be used by all other firms in the industry. By the very nature, new products take a while before their use becomes widespread. Therefore, the benefits of new products in terms of increasing aggregate output accrue only upon their complete diffusion in the economy. This process typically takes time. In the model it takes a minimum of one period ( which corresponds to a quarter) for new products to be fully diffused in the economy. I refer to this as "slow diffusion" as opposed to "instantaneous diffusion" ? 'For example, the seminal paper by Romer (1987) makes this assumption to study endogenous growth. 2In the latter, the creation of new products and their diffusion is contemporaneous. 71 In the model that I present below, each firm produces a unique product. Therefore, the birth of new products corresponds to the entry of firms. The advantage of this approach is that it allows us to capture the essence of the empirical findings that innovation rates are high among new firms ( see Acs and Audretsch (1988), (1989), (1994)) and that 55% of all entrants in the U.S. manufacturing industries are de novo firms (that is, new firms with new production facilities (see Dunne, Roberts, and Samuelson (1988)).3 I analyze the dynamic response of the economy with the above features. In particular, I am interested in understanding the role played by the slow diffusion of new products in propagating business cycle shocks. The motivation behind this paper is the finding of Cogley and Nason (1995) who point out that most real business cycle models have weak propagation mechanisms4. Recently, Burnside and Eichenbaum (1996) have examined the role of variable capital utilization rates in propagating the effects of shocks over the business cycle. Beaudry and Devereux (1995) introduce an intertemporal dimension to the technology available to firms. This channel affects factor utilization rates and through it, the strength of the propagation mechanism. Perli (1998) examines the role of increasing returns and home production. Cooper and Johri (1998) explore the relevance of learning-by-doing in the propagation of shocks. Overall, the research to identify important real propagation mechanisms is still an open area for research. I develop a multi-sector dynamic general equilibrium model which is calibrated to the U.S. economy. In the model, firms operate in a monopolistically competitive sector and produce intermediate goods. The intermediate goods are combined to produce a final output which is used both for consumption and investment. In another sector of the economy, new intermediate products or designs are developed using labour and capital resources, and a constant returns to scale technology. I refer to this sector as the 'innovation sector' of the economy. It takes one period for the new products to get diffused in the 3Moreover, it keeps the model analytically tractable. I do not model the locational or informational aspects of innovations. 4Zimmermann (1996) provides an extensive bibliography of of real business cycle models. 72 economy.5 The implication of this assumption is that the total number of products in the economy (or the product space) itself is a state variable and contributes to the dynamics of the economy. The new products enter the intermediate goods sector via the entry of firms and expand the product space of the economy. The size of a particular firm is measured by its output. The aggregate output in the economy depends on the size of the firms and the product space, both of which are endogenously determined in the model. I find that the qualitative dynamics of output, employment and investment are very different from a model in which there is instantaneous diffusion of new products. In the present model, the impulse response functions for these variables show the characteristic hump-shape observed in the U.S. data. In most models with weak internal propagation, consumption and employment move in opposite directions after the initial shock period. Slow diffusion of new products makes consumption and employment move together even after the period in which a shock is experienced. The impulse responses suggest that further quantitative exploration of this candidate propagation mechanism is warranted. The results also indicate that a multi-sector model is potentially a useful environment in which to study output dynamics. The organization of the rest of the paper is as follows. In section 2, I present the model. In section 3, I discuss the market clearing conditions that characterize the equilibrium of the economy and provide the intuition behind the propagation mechanism. In section 4, I discuss the calibration of the model. I report the results in 5. Finally, section 6 concludes.6 4.2 Model In this section I present a multi-sector dynamic model in which there is a final good sector, an intermediate good sector, and an innovation sector. The intermediate good sector is monopolistically competitive and each firm produces a unique product. The modeling strategy for introducing a monopolistically competitive sector closely follows Hornstein 5This assumption facilitates comparison with the instantaneous diffusion model. Allowing for slower-diffusion, several periods, is likely to strengthen the mechanism. 6 The appendix provides the steady-state calculations and the log-linearized version of the model 73 (1993) and Devereux, Head and Lapham (1996).7 The key difference between these models and the one developed here is that I explicitly introduce an innovation sector where new products are created using the available resources and are slowly diffused in the economy. The introduction of this sector adds an additional state variable in the model, namely the range of products available at a given time. 4.2.1 F i n a l G o o d Sector There is a single final good produced in a competitive market using the intermediate goods. The final good is both consumed and invested. The technology to produce this final good is given as yt = Ntx[[Ntmetdi\1/>>, P6(0,l) , (4.1) Jo where p is the elasticity of substitution between any two intermediate goods. This spec-ification of technology captures, in a simple manner, the notion that entrant firms make productivity enhancing innovations. To see how it works, suppose that the amount of intermediate good produced by each firm that gets used up in producing the final good at time t is the same across all firms. Also, let A = 0. I can now rewrite the expression for i - i final output as yt = Ntp Ntmt. An increase in the number of firms in existence at time t - — l raises the average productivity of the factors of production; N p represents the level of productivity enhancement. As new products get diffused, the primary inputs required to produce a given level of output falls for all the firms, thereby enhancing the total factor productivity. The above formulation has been used in the context of endogenous growth (see Romer (1987)), international trade (see Ethier (1982)), and more recently in explain-ing complementarities (see Matsuyama (1995)). The parameter A is used to control the degree of increasing returns. For instance, setting A = 1 — ^ , I get constant returns to specialization. 7Chatterjee and Cooper (1993) study the qualitative role of contemporaneous entry and exit of firms in the propagation of technology shocks. 74 The cost function associated with this technology is' where CY(Pt,yt) = ytNt\j\P/rl){p-1)/p, (4.2) Pt = NT~X[ j PP.HP-U](P-V/P. (4.3) Equation (3) simply indicates that the price of the competitively produced final good Pt is equal to the input cost index for intermediate inputs used in the production of the final good. Using Shephard's Lemma I can derive the conditional input demands:9 [ J o i v ^ A W ) ] 1 / p mj(Puyt,Nt) = y N t - ' J i , - (4.4) 4.2.2 Intermediate Goods Sector There exists a continuum, Nt, of firms (equivalently products) at time t. Each firm is monopolistically competitive and it produces a unique intermediate good using capital and labor as inputs. A representative firm i in this sector is characterized by a constant-returns-to-scale technology: m i t = z t W ' n " 0 < a < 1, (4.5) where ma is the firm's production, and ku and ha are the rented capital and hired labor services respectively. zt is a sector-wide technology shock that follows an AR(1) process of the form logzt = uz\ogzt-\ + et where et, is i.i.d. N ~ (0, a2) and 0 < UJZ < 1. There are no fixed costs of production as I discuss in Section 2 below. The cost function associated with this technology is given as: CM(wt,rt;mt,zt) = Arfw\-a^ (4.6) 8The cost function can be derived by solvingCy(Pt, yt) = Min{mu}i(_[0 N {/„ ' pum,itdi \ N?[fQ ' m^di}1 9The price elasticity of demand is given as -g^-^r = jhj Vj 75 where A ~ ( 1 - a)l-aaa' Again, using Shephard's Lemma, the conditional input demands are obtained as: M ^ ™ , ^ = ( ^ y ( ^ y ^ , ( 4 . 7 ) \ a J \wtJ zt (T^y J I T ( 4 ' 8 ) Each intermediate good producer takes the pricing decisions of other firms as given and solves the following profit maximization problem: m&x{pitm,it{yi., Pt, Nt) - C(wt,rt;m,t, zt)}. ( 4 . 9 ) Pu 4.2.3 Innovation Sector The innovation sector of the economy is characterized by a constant returns to scale tech-nology through which investment in new products is achieved. This technology uses labor and capital as inputs. I denote investment in new products as nt, while Nt is the total number of products in existence at time t. Again, the crucial aspect in this model is that new products get diffused after a delay of one period10. The implication of this assumption is that the product space itself becomes a state variable in the economy. Therefore, in this model, propagation of shocks is via both the capital accumulation and the endogenous expansion of the product space. The creation of new products follows the process Nt+1 = nt + ( 1 - Sn)Nu ( 4 . 1 0 ) where nt = etklthl-\ 0 < 7 < 1 - ( 4 . 1 1 ) 1 0Ambler and Cardia (1998) impose an exogenous one-period delay in entry. However, the aim of their paper is to explain the procyclicality of the share of profits in national income. 7 6 Here 6t is a technology shock affecting the innovation sector and it follows an AR(1) process of the form log (9t = LOQ log 9t-\+Tt where rt is identically and independently distributed with mean 0 and variance sigm.ag), and 0 < OJQ < 1. In every period a proportion 0 < 8n < 1 of the products fail and the firms producing these products exit. Note that in this model a ^ 7 . This difference implies that the factor intensities in the intermediate good sector (a) and the innovation sector (7)are different. This feature affects the intersectoral allocation of factors in a way that is important for the dynamic behavior of the economy. The cost function for this sector is given by CN(wurunt,Ot) = TrJwl-^, (4.12) where r - 1 ( 1 - 7 ) 1 - 7 7 1 ' As before, I obtain the following conditional input demands: hn(wt,rt;nt,et)= [ ^ — ^ Y ( - Y (4-13) 7 J \wtJ 0t 7 v \ 1 7 (wt\ 1 7 nt M ^ n ; n ^ t ) = ^ - 7 T ^ - ) j ^. (4.14) 4.2.4 Cap i t a l Accumula t ion Capital is accumulated by investing the non-consumed portion of the final good according to the following linear process: Kt+i = (1 - 6)Kt + It 0 < 6 < 1, (4.15) where 6 is the rate of depreciation of the capital stock. 77 4.2.5 Feasibil i ty Cond i t ion The total output produced in the economy equals its consumption and investment. yt = Ct + It. (4.16) 4.2.6 Representative Consumer-Household There is a representative consumer who receives utility from the consumption of the final good and from leisure. It has a total time endowment of 1 unit obtains income from three sources: wage income earned in the labour market; rental income obtained from the capital market; returns from the ownership of intermediate good firms. The preferences of this consumer are given by U(ct, ht) = logo* + 77log(l - ht). (4.17) Here ht represents the non-leisure time. The objective of this household is to choose sequences {ct, ht, it, ^t}tZo> faking {wt, rt, qt, ^t}tZo a s g i v e n , to maximize oo EQ[J2 0lU{cu ht)\KQ, N0], 0 < B < 1, (4.18) t=o where (KQ, HO) are given. given. The budget constraint faced by the household is Ct + kt+i+qtMt+l=wtht + (l+rt-6)kt + {TTt + qt{l-8n))Ht Vt. (4.19) Here N t + i denotes the number of shares this household purchases in the new firms, while qt is the value of an intermediate good firm at time t. The dividend return on each unit of shares purchased at t — 1 is 7r t, while qt(l — 6n) is the capital gain. Optimal household decisions obtain when = J _ . (4.20) r)Ct wt That is, within any period t, the household equates the marginal rate of substitution between consumption and leisure to their relative prices. The relative price of consumption 78 is 1 as the final good price is taken to be the numeraire. The household's optimal decision to save in the form of investment satisfies the Euler condition l = 0Et[(-^-)(l + rw-8)}. (4.21) Ct+l That is, the marginal loss in utility from saving one extra unit at time t must be equal to the marginal gain in utility from the return on saving at t +1. Since the household has two types of saving technologies available, the return on the them must be equalized according to the arbitrage condition Et[{^)Ct+l + qt+l{l-^)\ = M — ) ( 1 + n+1 - 6)}. (4.22) c-t+i Qt ct+i As mentioned above, there are no fixed cost of production in the intermediate goods sector. Hence the equilibrium number of firms is determined by this arbitrage condition (22) which is similar to a zero-profit condition in a model with contemporaneous entry and exit. To see this, consider the case where 8n = 8 and qt+\ = qt- In this scenario Tr t = qt indicating that a unit of investment in either sector brings in exactly the same return. 4.3 Market Clearing and Symmetric Equilibrium Conditions In a symmetric equilibrium of this economy all intermediate goods firms produce the same level of output, ma = m,t, and charge the same price pu — Pt- Their input demands are also identical, ku = kt and hn = ht. Profit maximization in the final goods sector implies marginal cost pricing. Taking the price in this sector as the numeraire, the condition- (3) implies 1 = Nt-Using the symmetry of intermediate good prices, I get the equilibrium relation between the relative price of the intermediate goods and the number of products (or equivalently firms) in existence as follows: Pt = N ^ ~ \ (4.23) / V% 7 9 The constant elasticity of demand facing each intermediate good firm gives a mark-up pric-ing rule where p~l is the mark-up. This follows from the Dixit-Stiglitz (1977) formulation of monopolistic competition followed here.11 = Art wt ( 4 2 4 ) pzt. The marginal cost pricing in the new firm sector yields « = (4-25) while the final output in this symmetric equilibrium is given by yt = mtNt+K (4.26) The market clearing condition in the factor market may be written concisely as rNt Kt = h= / kltdi + knt = NtM + knt, (4.27) Jo rNt Ht = ht= / hitdi + hnt = Nth\ + hnt, (4.28) Jo . •10 where Kt and Ht are aggregate capital stock and employment respectively, and superscript i denotes the intermediate good sector. Using symmetry and the profit maximization conditions in the final goods sector (23), the intermediate goods sector (24), and the new firm sector (25) the expressions for the equilibrium factor prices can be written in terms of (qt,Nt,zu6t) as wt{quNt,zt,et) = T ^ i ^ ^ q f ^ N ^ ' ^ ^ z f ^ e f ^ , (4.29) and rt(qt,Nt,zt,0t) = r ^ i ^ ^ q p N ^ l ^ z ^ . (4.30) 1 1 As mentioned earlier, the interpretation of the term 'new product' includes the notion of 'distance' or 'location' - a feature non-existent in the Dixit-Stiglitz framework. This feature is, however, present in the locational models in the industrial organization literature. Recent work by Weitzman (1994) makes use of increasing returns to specialization to examine the relationship between these models. 80 Combining the equilibrium factor prices with the factor market clearing conditions the expressions for output per intermediate good firm (m,t), the net investment in new products (nt), and the profit per firm (irt) can be obtained. These expressions are a function of aggregate capital stock (Kt), aggregate employment (Ht), price of the firm (qt), the measure of firms (Nt) and the shocks. The expressions are: l - Q f \ I 1 i» 1—a \ 1 1—1 1 — a <* (A I 1 1) ( A ) 1 7 ° C3KtqraNt " a " 7 9?~a - CiHtq?-*1 Nt " 7 _ a z?-°dta-y " " = : : — T : : _ (4.31) where CA I 1 1)( ~* ) ~* Q i — 7 (A 1 1 l ) f 1~~ f) 1 ~ " Y 1 — Q f «7 where and Profits are given by a y / I > \ 7 - » 5^ I - a \ A C E = [ — [A 7r t(.) = ( l -p ) iV t A + "" 1 m t ( . ) . (4.33) 81 4.4 Equilibrium Characterization In the symmetric rational expectations equilibrium the per-capita variables and aggregate variables are identical. That is, ct — Ct,ht = Ht,kt = Kt, and ~Rt = Nt. Using the aggregate variables and the expressions for u>t, rt, mt, nt, and 7rt from the previous section, I can characterize the equilibrium of this economy in terms of [C, H, K, q, N] as follows:12 Ht = l- . y flV (4-34) wt\qt, Nt, zt, dt) l = 3Et[{-^)(l + rt+1(qt+i,Nt+i,zt+1,6t+i)-6)], (4.35) E t [ { a ) ( ! r ± t l i : ) ± M u i ^ ) ] = m ^ ) { 1 + r t + l f g t + l t N t + l i Z t + l t e t + l ) _ s ) ] t Of+i qt Ot+i (4.36) m,t(Kt, Ht, qt, Nt, zt, 6t)Nt+> = Ct + Kt+1 - (1 - S)Kt, (4.37) and nt(Kt, Ht, qt, Nt, zu 0t) = Nt+1 - (1 - Sn)Nt, (4.38) where (34) represents the consumption-leisure tradeoff, (35) is the Euler equation for op-timal investment decision, (36) is the arbitrage condition, (37) represents the aggregate feasibility condition taking into account the equilibrium output and (38) is the equilibrium law of motion for new firm creation. To gain some insight as to how the hump-shape response of output yt arises in this framework I rewrite equation (37) when A = 0 as mtNt,Ntp . Here Ntp may be thought 1 2 The 'dual' approach followed in this paper allows us to characterize the equilibrium of the economy in terms of aggregate employment and aggregate capital stock. An excellent exposition of this approach is given in Hornstein (1993). 82 of as the productivity index. At time t, the number of firms in the economy's intermediate good sector is fixed. When there is a positive productivity shock, yt increases as interme-diate good firms hire more labour to increase their output mt. But there is also creation of new firms that become productive at time t + 1. So even if investment declines mono-tonically after the period of shock, aggregate output rises on account of an endogenous expansion in the productivity index, hence propagating the effect of time t shock. 4.5 Calibration and Results The equilibrium conditions characterized in the previous section are nonlinear. To study the dynamic behaviour of this economy, I first linearize the conditions around the steady-state values and write the linearized system as Ms*Et[St+i] = Mc*St + Re*Zt (4.39) where St+i = (Ct+i> Qt+i, Kt+i, Nt+\)' • In the vector St, C and q are the co-state variables and, K, and N are the state variables at time t. Ms and Mc are 4x4 matrices of parameters and Re is a 4x2 matrix. Zt = (zt,0t)- All hatted variables are in terms of percentage deviations from their steady state values.13 The delay of one period in the entry process makes the number of productive firms, at a given point in time, a state variable. An additional set of linear equations that would determine the remaining variables is given by Wt = nSt + Ra*Zt, (4.40) where Wt = (Ht,yt,wt,ft,,Pt,^t,^,t,nt) , Q, is an 8x4 matrix of parameters, and Rs is an 8x2 matrix. I focus on the saddle path stable steady state. The parameter values used here ensure that the economy does not display explosive behaviour, nor does it have indeterminacy.14 The numerical procedure used to solve the model follows the methodology 13see Appendix for details. Campbell (1994) gives a detailed exposition of a linearization technique. I 4Since there are four state variables in the model and two of these are predetermined, two of the four eigenvalues are stable. This implies that the convergent subspace is two dimensional. Hence, the equilibrium path is a stable manifold for the calibrated values of parameters. 83 Table 4.1: Calibration Parameter Value 1 a Capital intensity in the intermediate good sector 0.36 2 7 Capital intensity in the innovation sector 0.64, 0.8 3 1 p Mark up 1.11 4 Q Discount rate 0.99 5 v Weight on leisure in preferences 2 6 8 Depreciation of capital 0.025 7 8n Product failure or bankruptcy 0.025 8 Uz Persistence of shocks in the intermediate good sector 0.95 9 CO0 Persistence of shocks in the innovation sector 0.95 10 crz Volatility of shocks in the intermediate good sector 0.007 11 0-0 Volatility of shocks in the innovation sector 0.007 of King, Plosser and Rebelo (1987) There are eleven parameters in this model that have to be calibrated: [a, 7, p, B\T], 6, 6n,UJZ, LUQ, az, OQ}. In this model, the intermediate goods sector is labor intensive. The share parameter for capital in this sector at a = 0.36 (see Prescott (1986)). The weight on leisure in the preferences is set at 77 = 2, the subjective discount rate is 3 = 0.99 and the rate of capital depreciation, 8 = 0.025. These values are as used in Hansen (1985). There is a one-to-one correspondence between the degree of increasing returns to specialization ^ — 1 and the mark-up in the intermediate goods sector j. Following the recent empirical evidence of Basu and Fernald (1995) favouring small mark-ups, I set p = 0.9, which implies a mark-up of 1.11. The two parameters 7 and 5n are not directly calibrated to data1 5. The death of products corresponds to the exit or bankruptcy of firms. From the point of view of the households, firms that create new products are also an asset, just like capital. I therefore equate the depreciation of capital to death of firms. That is, 8n = 8— 0.025. One important assumption that I have to make is that the new firm creation sector is relatively capital intensive. This issue is ultimately empirical, but it is not unreasonable to assume that the innovative sector of the economy requires relatively more capital. I report 1 5 In future work I plan to explore the implications of enndogenizing delta, and deltan along the lines of Greenwood, Hercowitz, and Huffman (1988). 84 the results for the case where 7 = {0.8, 0.64}.16 In the case where the factor intensities are identical across sectors (0 = 7), perfect reallocation of factors takes place instantly in response to the technology shocks. This reallocation does not affect the wage or the interest rate, which are determined by technology alone. This case is similar to the special case that Devereux and Love (1994) consider in a two-sector model of endogenous growth. In their model, identical factor intensities across sectors completely eliminate any transitional dynamics. To see how this works, I combine the profit-maximization conditions in the final good, the intermediate goods, and the new firms sector to obtain xf'i_1 = Pjfc-That is, the relative price of outputs of the two sectors depends only on the mark-up and the two shocks. Also, as in the one-sector RBC model, the following condition holds: j± = (^jz^j jf- The production possibility frontier for the output of the two sectors, Ntm.t and nt, is linear. In response to an aggregate technology shock to the intermediate good sector, the production possibility curve swivels out. The swiveling of the PPF takes place as 0t ^ zti. With a single shock the shift will be parallel to the original one. Thus more intermediate goods are produced as labour and capital move out of the new firm sector. Since is predetermined, qt increases instantly to balance the arbitrage condition. In this process, m,tNt increases and nt decreases. In Tables 2 and 3 I present some key model statistics.17 Overall, the model does fairly well in producing contemporaneous correlations and relative volatility. The volatilities of consumption, investment, and new firms are higher relative to the data. This feature is reflective of the fact that the present model is a multi-sector model with factors moving freely (that is, there are no adjustment costs) across sectors. The main results of this model are in terms of impulse response functions generated for 1 6It turns out that the capital intensity of this sector has to be sufficiently different from that of inter-mediate goods sector for the stability of the model. The critical value of the capital intensity of the new firm sector is 7C=0.54. This implies that (7 — a) > 0.18. The values for 7 used are (0.64, 0.8). 7 = 0.64 corresponds to the case where 7 = 1 — a. Benhabib, Perli, and Sakellaris (1997) find a similar result regarding the stability of a multi-sector model. 17A11 variables for the US economy are taken from the Basic Economic (formerly, CITIBASE) dataset. n in the US data refers to the New Business Incorporation series. Both real and simulated data are logged and HP filtered. 85 Table 4.2: Contemporaneous Correlations Model Statistics 1 US Data Model Corr(y,C) 0.78 0.36 Corr(y,i) 0.91 0.88 Corr(y,n) 0.56 0.36 Corr(y,7r/y) 0.78 0.98 Tab e 4.3: Relative Volatility Model Statistics 2 <K 1 1.42 <l< 1.19 °hl< 1.06 <l< 1.91 1% technology shocks. The persistence parameter for the economy-wide technology shock (u>z=u)0) is 0.95. I compare the results with the model of Devereux, Head, and Lapham (1996).18 In their model there are increasing returns to specialization and instantaneous diffusion of products. Hence, their model serves as a benchmark to assess the dynamics introduced by slow diffusion. 4.5.1 Economy-wide shock: uz=ue= 0.95 In this model there are two production sectors so an economy-wide technology shock affects both sectors. This also facilitates comparisons with the Devereux, Head, and Lapham (1996) model where the diffusion of products is instantaneous. The results are reported in Figures 4.1 - 4.6. Figures 4.2 and 4.3 are for the case where 7 = 0.8 and Figures 4.4 and 4.5 are for the case where 7 = 0.64. The first point to note is that the qualitative response of output and employment is very different relative to a model in which there is instantaneous diffusion of new products. Figure 4.6 presents the results from the Devereux, Head, and Lapham (1996) model in which there is instantaneous diffu-1 8 The focus of Devereux, Head, Lapham (1996) is on the measurement of technology shocks. 86 sion of new products. In the instantaneous diffusion model, output declines monotonically after the period in which the economy is hit with a shock. In the present model with slow diffusion, the impulse response for output displays a characteristic hump-shape (See Figure 4.1). For Figure 4.1 the parameter values are 7 = 0.8 and 8n = 0.025. The response of the slow diffusion model is similar to what is observed in the data. The reason for the output response in the model is as follows: In the model with slow diffusion, there are two components to the propagation mechanisms, namely, capital accumulation and slow product diffusion. An aggregate shock increases productivity in both sectors. Output of the intermediate sector rises due to an expansion in the size m-t, of existing firms. I refer to this as the adjustment on the intensive m.argin. This expansion in firm-size raises aggregate output in the current period, since the number of firms is fixed. Both consumption and employment rise, and the rise in employment boosts investment. Also, investment in the innovation sector goes up, which increases the range of intermediate goods that are available in future. I refer to this as adjustment on the extensive margin. Since there is slow diffusion of new products, future output rises due to the endogenous expansion in productivity that results from increasing returns to specialization.19 In period t + 1, a large proportion of the increase in capital stock is absorbed by the capital intensive innovation sector. This leads to a further increase in investment in this sector. Employment rises in this period. This response of employment is very different from 19Aggregate output depends both on the firm-size, m t , and the total number of firms (or products), Nt-At the time of the shock Nt is predetermined. Therefore, there is an increase in the firm size. In the following period more new products are diffused so that Nt rises. This expansion of the product space has two effects on the firm size. Each existing firm is more productive due to increasing returns to specialization and hence uses less resources to produce a given level of output. This productivity effect tends to increase firm size. However, there are more firms in existence in the period following the shock. Hence a given amount of resources have to be divided among a larger number of firms. This effect can be thought of as the congestion effect which tends to decrease firm size. For a mild degree of increasing returns to specialization, the congestion effect dominates. Therefore I do not see a hump-shape in the firm size. When I experimented with increasing the bankruptcy rate from Sn = 0.025 to 5n = 0.03, the firm size in fact increases since the given amount of more productive resources are divided among fewer firms (the impulse responses are not reported here but are available upon request). This dampening of the congestion effect generates a hump-shape in the response of firm size to shocks. The fact that the existing firms experience an increase in their output during periods of bankruptcies is a testable prediction of the model. One can examine the market shares of surviving firms in an industry and see if they shrink or expand in periods when bankruptcies are high. 87 models with weak propagation mechanisms in which consumption and employment move in opposite directions after the initial period of shock. The reason for this behaviour is that the atemporal trade-off between consumption and leisure, represented by (20), has to be satisfied every period. Since consumption continues to increase, employment must fall to satisfy the equality. A fall in employment implies a fall in output and consequently output does not display a hump-shape response. In the present model, however, consumption and employment move together even after the period of the shock. The reason is that wages increase for several periods as a result of an improvement in aggregate productivity due to increasing returns to specialization. Therefore households supply more labour even after the period of the shock and both consumption and labour move together for a few periods. The response of consumption and employment in this model resembles the finding of Perli (1998). 4 . 6 Conclusion The qualitative results of this paper suggest that slow diffusion of new products in the economy could itself be a vehicle for shocks to propagate in the economy. Relative to a model where there is instantaneous diffusion of new products, the present model displays interesting output dynamics which are qualitatively similar to those observed in US data. In order to keep the analysis tractable, I ignored any potential constraints faced by firms in the innovation sector. In reality, the firms in this sector are likely to face financing-constraints. This may hinder productivity enhancing innovative activity in the economy. Given the importance of the innovation sector for the results of the model, it will be interesting and useful to conduct an detailed analysis of this aspect of the economy and study the implication for policy. This investigation is left for future work. Impulse Response of Output Slow Diffusion Vs Instantaneous Diffusion Figure 4.1: Impulse Response of Output: Slow Vs. Instantaneous Diffusion 89 Figure 4.2: Impulse Responses: 7 = 0.8, Sn = 0.025 90 Figure 4.3: Impulse Responses: 7 = 0.8, Sn = 0.025 91 Figure 4.4: Impulse Responses: 7 = 0.64, 8n — 0.025 92 Figure 4.5: Impulse Responses: 7 = 0.64, 6n = 0.025 93 9 4 Appendix To solve this model I first compute the deterministic steady state of the model. There are eleven endogenous variables [C, H, K, N, u>, r, q,p, m, n, TT]. The values are obtained by solving the following set equations: p ^ A ^ + p - 1 (4.41) p = (4.42) P = I V ™ 1 " 7 (4.43) K = (-^-)l-<*(-)l-am,N + (-2— ) 1 - T ( - ) 1 - T n (4.44) 1 — a r 1—7 r H = (L-2.)°(L)o>mN + (i_2 ) 7 ( H ) 7 n (4.45) a w 7 ui TT = (1 - p)NX+"1m (4.46) H = l - ^ (4.47) it; r = ^ + 5 - 1 (4.48) 95 Table 4.4: Steady-State Shares Shares C/y wJ-l V rK y y 0.699 0.30 0.586 0.31 0.1 r + 6n — 6 C = m,NX+p - 8K (4.49) (4.50) n = SnN (4.51) Using (39) and (40) I get w = = w(N) Combining (41), (44), and (47) I can get m = (r-s+^)Tr^ 1 = m(N) (l-p)N  + P From (45) and (48) I get H = 1 - vimN^J-SK) = H^R^ ] V ) Using H(K,N) and (43) to obtain K = ( £ ) ( + ( I=2 ) « ( i ) « m i V + ( i = 2 ) 7 ( i ) 7 5 n j v K(N) Finally, K(N) and (42) yield a single nonlinear equation in TV that can be solved numeri-cally. F(N) = [(^)Q - (f )(I^)1"a] (f)-am,N+ [ ( ^ - (f)^6nN-l + mnl^i = 0 Steady-state shares: The above values in Table 2 are for 7 = 0.64 and 6n = 0.020. The values for 7 = 0.8 are very similar. 96 The Linearized Model: The linearized version of the model around the steady state could be written as Wage wt = hqt + b2hNt + b3zt + b\6t (4.52) Interest rate h = hqt + b2b5Nt + b5£t + bjt (4-53) m,t rht = emKKt + emHHt + dxqt + d2Nt + d3zt + dA0t (4.54) nt nt = enKKt + enHHt + d5qt + deNt + d7zt + d&8t (4.55) T?t = b2Nt + rh,t (4.56) Consumption-employment tradeoff Ht = (^-)(wt-Ct) (4.57) Consumption-investment decision Ct+i - b0rtXi = Ct (4.58) Arbitrage condition 6io.7rt+i + bnq{+i - qt - bon+i (4.59) Resource constraint rht + (A + -)Nt = scCt + ^Kt+i ~ (^)siKt (4.60) p o o 97 Net investment in new products : x •"'•-t-J- v c On 0n Here, 60 = (1-/3(1 -6)) h = — j- a—7 b2 = A + i - 1 6 3 &4 7 7—a 1-a 7—a i=2 a—7 6 6 = 5 = ^ a 7—a &8 = a—7 a 7—a 6 1 0 = l - P ( l - 8 r , bn = - r5n) * C — y n t = - ( V ^ ) i V t (4.61) 98 Z-nK d\ = b4emK + b1emH da = ( ^ 6 - l)emK + ( M 7 - l)em// ds = b5emK + b3emH d^ = b±em.K + b\emn d.5 = bsenH + bgenK de = b2henH + b2b5enK dq = hCnH + henK dg = b\enH + bAenK Substituting out the expressions for wt, rf+i, Ht, m,t, nt, and irt+i I can write the linearized system as: Ms * Et[St+i] = Mc*St + Re*Zt 99 where St+i = (Ct+i, <?t+i, Kt+i, Nt+i) , St is same as above but at time t. Ms and Mc are 4x4 matrices of parameters and Re is a 4x2 matrix. Zt = (zt,9t). All (X) variables are in terms of percentage deviations from their steady state values. Among the four variables, Kt and Nt are predetermined state variables and Ct and qt are jump variables. Additional set of linear equations that would determine the remaining variables is given by: Wt = nSt + RS* Zt (4.62) where Wt = (Ht,yt,wt,ft,Pt,^t,m,t,nt)' and Q is a 8x4 matrix of parameters and Rs is a 8x2 matrix. 100 Chapter 5 Conclusion A challenge faced by modern business cycle theory is to understand mechanisms that can explain the persistent nature of output and real exchange rate fluctuations. As a result, considerable amount of effort has been devoted towards investigating both nominal (sticky price) and real propagation mechanisms that can make the effect of small shocks to the economy persist for a long time. In the literature that seeks to explain the persistent output and real exchange rate fluctuations, the sticky price framework has received considerable attention. In this thesis I have tested the predictions of the sticky price model for output and real exchange rate dynamics. The central idea is that in high inflation countries price stickiness should be less important and therefore output and real exchange rates fluctuations should display less. If this is dependence of price stickiness on the inflationary environment holds, then the sticky price model implies an inverse relationship between persistence in both output and real exchange rate fluctuations and the inflationary environment. In Chapter 2 and Chapter 3 I test predictions for output and real exchange rate dynamics respectively. The empirical analysis reveals that the inverse relationship is, in general, statistically insignificant in the international data for both output and real exchange rate dynamics . Furthermore, I find that in the empirical implementation of the hypotheses it is important to take into account the within-country time variation in inflation. I use two separate ways of addressing this issue. First, I identify the inflationary environment within a country by the long-run movement in its inflationary experience. Second, I exclude episodes of hyperinflation. I find that if one ignores the within-country time variation and use average inflation to summarize the inflationary environment then, in the full sample, there inverse 101 relationship is statistically significant. For both output dynamics and real exchange rate dynamics I find that this statistical significance of the inverse relationship is driven entirely by a few episodes of hyperinflation. The results suggest that only episodes of hyperinflation, which are periods of extreme monetary instability, are informative on the predictions of the staggered sticky price frame-work. The persistence in output and real exchange rate fluctuations is less only in periods of hyperinflation. Therefore, the results raise a problem for the sticky price framework as a microfoundation for explaining output and real exchange rate fluctuations. The results also point towards investigating the role of market structure and market incompleteness in causing persistent fluctuations and their relationship with inflation. Future research on this issue would be quite useful. In Chapter 4, I qualitatively explore a potential real propagation mechanism. I consider the role of slow diffusion of new products in propagating technology shocks. Towards this end, I develop a multi-sector DGE model calibrated to U.S. data. The qualitative results from this model are encouraging. I find that, relative to a model where there is instantaneous diffusion of new products, slow diffusion in fact contributes to output dynamics in a manner which is similar to what is observed in the U.S. data. 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