Dynamic Olley-Pakes Decomposition with Entry and Exit

Transcription

1 Dynamic Olley-Pakes Decomposition with Entry and Exit Marc J. Melitz Princeton University, NBER and CEPR Sašo Polanec y University of Ljubljana and IER March 24, 2008 Abstract This paper shows that widely used decompositions of the change in aggregate productivity index into contributions of di erent drivers of growth tend to underestimate the contribution of reallocation between surviving rms and overestimate the contribution of entering rms. Building on the cross-sectional decomposition proposed by Olley and Pakes (1996), we propose a new decomposition that remedies this problem. The proposed decomposition expresses its components in terms of moments of joint size and productivity distributions for three sets of rms: survivors, entrants and exitors. Each of these sets of rms contributes to the change of aggregate productivity in a direct way by improving the average productivity and indirectly by improving the covariance between productivity and market shares. Using Slovenian manufacturing data, we compare the results of di erent decompositions and nd that new decomposition gives more realistic estimates of direct and indirect contributions of entering, exiting and surviving rms. Keywords: decomposition, aggregate productivity, distributional moments JEL Classi cation Numbers: C10, O47 1 Introduction Theoretical literature distinguishes between two drivers of change in aggregate productivity. The rst is a process of productivity improvements within surviving rms and the second is a process of reallocation of inputs and outputs between surviving, entering and exiting rms. In order to distinguish between the contributions of these processes, Baily, Hulten and Campbell (1992) proposed the rst method that decomposes the change in the standard aggregate productivity Department of Economics, Princeton University, Fischer Hall, CORRECT. mmelitz@princeton.edu. y Faculty of Economics, University of Ljubljana, Kardeljeva pl. 17, 1000 Ljubljana. saso.polanec@ef.unilj.si. 1

2 index. Since their method yields biased contributions for entering and exiting rms, Griliches and Regev (1995) and Foster, Haltiwanger and Krizan (2001) proposed improved varieties of Baily et al. decomposition. Despite signi cant reductions in measurement biases, these two widely used decompositions did not eliminate them completely. In this paper we show that both methods underestimate the contribution of surviving rms and overestimate the contribution of entering rms. We also show that the Griliches and Regev method yields lower bias in measurement of contribution of entering rms, but at the cost of greater bias in measurement of contribution of exiting rms. We attribute these biases to the fact that both decompositions distinguish between di erent components by using xed weights. As a consequence the two methods use ill-suited reference productivity levels in evaluation of contributions of entering and exiting rms. In order to eliminate these biases, we propose a new decomposition of the change in aggregate productivity index. In building this decomposition, we exploit the fact that the aggregate productivity of a group of rms can be expressed as a weighted average of aggregate productivities of subgroups of rms and the well known Olley- Pakes decomposition, which decomposes the aggregate productivity into average productivity and covariance between weights and productivity. In this way, unlike Foster et al. and Griliches and Regev decompositions, the proposed decomposition does not keep track of rms over time, but instead captures only those reallocations that also change the moments of distributions. An important feature of the proposed decomposition is that it distinguishes between average e ect from reallocation for surviving, entering and exiting rms. The decomposition yields six components, two for each set of rms. For surviving rms, we distinguish component that measures the within rm productivity growth calculated as a change in average productivity and component that measures the contribution of a change of covariance between productivity and market shares. For entering and exiting rms, we distinguish between components that re ect contributions of average productivity di erences between these and surviving rms and components that re ect contributions of respective di erences in covariances. We use real rm-level data to illustrate di erences between our method of decomposition and the methods of Foster et al. and Griliches and Regev. Our method yields signi cantly lower contribution for entering rms and signi cantly higher contribution for surviving rms than the other two methods. The Griliches and Regev method yields lower bias for entering rms and higher for exiting rms than the Foster et al. method. We also nd that these biases increase with length of time span over which they are calculated. 2

3 Our e ort to correctly measure the contribution of di erent processes is not alone. Recently, Petrin and Levinsohn (2005) proposed an alternative method that decomposes the change of Tornquist-Divisia index. They motivate use of this index with argument that the change in the standard aggregate productivity index is a poor measure of welfare. However, since they decompose the change in aggregate productivity growth rather than the change in aggregate productivity, they are unable to correctly measure the contributions of di erent sets of rms to the change in aggregate productivity. The remainder of the paper is organized in the following way. The next section reviews existing decompositions. In the third section we outline the proposed decomposition. In the fourth section, we illustrate the di erence between this method and alternative methods via using rm-level data and in the fth section, we consider the relationships between the components of new decomposition at the sectoral and industry level. The last section concludes. 2 Review of decompositions The methods that decompose the change of aggregate productivity indices into contributions of di erent processes and/or di erent sets of rms are relatively recent in the economics literature, coinciding with development of theories of economic growth with creative destruction that emphasize the importance of reallocation for the aggregate productivity growth. These decompositions can be grouped by two criteria: whether they use the standard index of aggregate productivity or not and whether they use xed weights or distributional moments in calculation of components. Following the seminal contribution of Baily, Hulten and Campbell (1992), the majority of methods (Griliches and Regev, 1995; Foster, Haltiwanger and Krizan, 2001; Olley and Pakes, 1996) decompose the change of the standard index of aggregate productivity: t = X i2 t s it ' it ; (1) where s it and ' it denote the share of rm i in an industry in period t (e.g. nal goods market and employment) and its index of productivity, respectively, and t denotes the set of active rms in this period. On the other hand, motivated by discrepancies between the standard index of aggregate productivity and the measure of welfare, Petrin and Levinsohn (2005) decompose the change of the Tornquist-Divisia index. According to the second criterion, the methods of Baily et al. (1992), Griliches and Regev (1995), Foster et al. (2001) and Petrin and Levinsohn (2005) use xed weights 3

4 in calculation of components, whereas Olley and Pakes (1996) use distributional moments. In the remainder of this section, these methods are discussed in detail. Baily et al. (1992) propose to decompose the change of aggregate productivity index between two periods in the following four components: 2 1 = X i2s s i1 (' i2 ' i1 ) + X i2s (s i2 s i1 )' i2 + X i2e s i2 ' i2 X s i1 ' i1 ; (2) i2x where S, E and X denote the sets of surviving, entering and exiting rms, respectively. The rst term on the right-hand side of equation (2) is called "the within component" as it aims to capture the contributions of productivity improvements of surviving rms. These improvements are weighted by xed market shares from initial period. The second term, the "between component", measures the contribution of shifts of market shares between surviving rms weighted by end period productivity indices. The last two terms measure the contributions of entering and exiting rms, calculated as sums of cross products between rms market shares and productivities. The way these contributions are calculated is the main objection against this decomposition as it yields positive and negative contributions for entering and exiting rms, respectively, as long as there are some rms that decide to enter and exit. In order to reduce these biases, Griliches and Regev (1995) and Foster et al. (2001) propose alternative decompositions, both based on the Baily et al. (1992) decomposition, that introduce reference productivity values in calculation of contributions of entering and exiting rms. The Griliches and Regev decomposition is given by: 2 1 = X s i (' i2 ' i1 ) + X i2 s i1 )(' i ) + (3) i2s i2s(s + X X s i2 (' i2 ) s i1 (' i1 ); i2e i2x where s i = (s i1 + s i2 )=2, ' i = (' i1 + ' i2 )=2 and = ( )=2: The terms of this decomposition have the same economic interpretation as those of Baily et al., although the expressions of components are quite di erent. The productivity improvements of surviving rms are now weighted by time averages of market shares instead of initial period market shares, whereas the shifts of market shares are weighted by the di erence between time averages of individual and aggregate productivity indices. These changes in terms that measure contributions for surviving rms are 4

5 also re ected in terms that measure the contributions of entering and exiting rms. In contrast to the Baily et al. decomposition, the contribution of entrants is now positive only if the aggregate productivity index of entrants in period 2 exceeds the time average of aggregate productivity index for all active rms and the contribution of exitors is negative only if the aggregate productivity of exitors in period 1 exceeds the time average of aggregate productivity index for all active rms. 1 These modi cations reduce the biases inherent in measurement of contributions of entrants and exitors, although, as we argue below, not completely. Foster et al. (2001) found an alternative way to decompose the change of aggregate productivity index and introduce the reference productivity level in terms that capture the contributions of entrants and exitors: 2 1 = X i2s s i1 (' i2 ' i1 ) + X i2s(s i2 s i1 )(' i1 1 ) + + X (s i2 s i1 )(' i2 ' i1 ) + X s i2 (' i2 1 ) (4) i2s i2e X s i1 (' i1 1 ): i2x Their decomposition preserves the rst term of Baily et al. decomposition and modi es all the remaining components. The process of reallocation of market shares between surviving rms is captured in two components. The rst is called the "between component" and measures the contribution of shifts in market shares weighted by the di erence between initial individual and initial aggregate productivity index. This component is positive only when on average rms market shares move in line with deviation of initial individual productivity index from initial aggregate productivity index. The second is the "cross or covariance component" and measures the covariance between changes of individual market shares and changes of individual productivity indices. This term is positive if changes in market shares and productivity indices move in the same direction and vice versa. The last two terms measure the contributions of entering and exiting rms. In contrast to the Griliches and Regev decomposition, the Foster et al. decomposition yields positive contribution for entrants if the aggregate productivity index for entrants exceeds the period 1 aggregate productivity index of all active rms (including exitors) and negative contribution for exitors if the aggregate productivity index for exitors exceeds the period 1 aggregate productivity index of 1 The contributions of entrants and exitors can be rewritten as s E2( E2 ) and -sx1( X1 ), where se2 and s X1 denote the aggregate market shares of entrants and exitors and E2 and X1 denote the aggregate productivity indices of entrants and exitors. 5

6 all rms. While both methods reduce the measurement biases, neither of the two eliminates them completely. Since this is the key motivating fact for our proposal of an alternative decomposition, we characterize these biases for a simple stylized example. Suppose we have only one surviving rm that exists forever and a set of one period rms that enter and exit in each period. The total number of active rms in each period is thus equal to 2. Assume further that productivity indices of all rms increase by a constant in each period. 2 Formally, the law of motion for rm i is given by: ' it+1 = ' i1 + t; where ' i1 and ' it+1 denote productivity indices in periods 1 and t + 1. The index i refers to either surviving (i = S), entering (i = E) or exiting rm (i = X). We also assume that the market share of the surviving rm does not change over time, s St = s S ; which implies equality between market shares of entering and exiting rms in all time periods, s Et = s Xt. Lastly, we assume that the productivity index of exiting rm in period 1 equals to the aggregate productivity of surviving rm in period 1, ' X1 = ' 11. Given these assumptions the Foster et al. decomposition for the change of aggregate productivity between periods 1 and t + 1 yields two components with non-negative values: the contribution of surviving rm is equal to s S t and the contribution of entering rm is equal to (1 s S )t. On the other hand, the Griliches and Regev decomposition yields three components with non-negative values: the contribution of surviving rms is also equal to s S t, whereas the contributions of entrants and exitors are both equal to (1 s S )t=2: Since productivity indices of exitors and entrants match respective productivity indices of survivors in the initial and end periods, unbiased measures of contributions of these rms should be equal to zero. Hence the Foster et al. decomposition overestimates the contribution of entrants, whereas the Griliches and Regev decomposition overestimates the contributions of both entrants and exitors. The size of these biases also increases with time span (t) as productivity of all sets of rms increases over time. More recently, Petrin and Levinsohn (2005) proposed an alternative decomposition. As noted above, they recognize the fact that the change of the standard aggregate productivity index may be a poor approximation for the change in welfare that arises from rms productivity improvements. For this reason, they propose a decomposition of a measure of aggregate productivity change that 2 This assumption is justi ed by empirical regularity of stationary di erence between average productivities of entrants and surviving rms for manufacturing sector. 6

7 is more closely related to the change of welfare, the Tornquist-Divisia index: d = NX s vi d ln! v i ; (5) i=1 where d ln! v i = of rm i value added de ned as d ln! i (1 s Mi ) is input corrected measure of the change in productivity. s v i is the share s vi = P iy i P Pi Y i : where P i denotes the price of nal goods and Y i denotes real nal demand (or value added) from plant i and Y i = Q i P N j=1 M i j ; where M i j is demand for intermediate produced by rm j. Unlike decompositions that decompose the change of the standard aggregate productivity index, Petrin and Levinsohn (2005) propose to decompose the change of the productivity growth rate: NX d 2 = d( s vi d ln! v i ); (6) which can be estimated as the di erence in two average-share log-change indices: i=1 XN 2 i=1 s vi ;t+2 + s vi ;t+1 (ln! v i;t+2 2 ln! v i;t+1) XN 1 i=1 s vi ;t+1 + s vi ;t (ln! v i;t+1 ln! v 2 i;t): (7) This equation decomposes into a "productivity" term, a reallocation term, and a "net entry" term. The set of rms that exist in periods t, t + 1 and t + 2 is denoted S (for survivors), and each of these rms contributes a productivity component and a reallocation component to the growth in aggregate productivity. Firms that exist only in periods t and t + 1, or only in periods t + 1 and t + 2, contribute to the overall change in (7), but only through net entry term described below. The productivity term is: X i2s s vi;t+2 + 2s vi;t+1 + s vit (ln!v i;t+2 4! v i;t+1 ln!v i;t+1! v ); (8) i;t where each surviving rm contributes to the growth in the rate of productivity growth. The weight in the aggregation to the industry level is an average over the three time periods of the rm s share in value added, where t + 1 gets twice the weight of period t and period t + 2. The reallocation 7

8 term is given by: X i2s (ln!v i;t+2! v i;t+1 + ln!v i;t+1! v )=2 (s vi;t+2 s vit )=2: i;t The term on the right gives the change in the share of value added from period t to period t+2:the last term captures the contribution of net entry: X i2t+1;t+2;not t X i2t;t+1;not t+2 s vi;t+2 + s vi;t+1 (ln! v i;t+2 2 s vi;t+1 + s vi;t (ln! v i;t+1 2 ln! v i;t+1) ln! v i;t): The net entry is measured as the di erence between those rms absent in period t (but present in periods t + 1 and t + 2) and those absent in period t + 2 (but present in periods t and t + 1). Since the share-weights on either side of the di erence do not sum to one, this term can be driven both by the prevalent growth rates of entrants and exitors and by their mass in the population. While Petrin and Levinsohn (2005) raise an important issue of the choice of adequate aggregate productivity index, they do not provide a solution to the outstanding problem of measurement biases in existing decompositions. They decompose the change of the Tornquist-Divisia index, which itself is de ned as a weighted average of changes in rms productivity indices. Consequently, their method measures the contributions of di erent processes to acceleration or deceleration of the change of aggregate productivity index instead of contributions to the change of aggregate productivity itself. The last decomposition that is commonly used in empirical literature was suggested by Olley and Pakes (1996). Unlike the methods described above, their decomposition distinguishes between the contributions of productivity improvements and reallocation using the moments of the joint distribution of rms productivity indices and market shares. The static Olley-Pakes decomposition splits the aggregate productivity index in two components: t = ' t + X i (s it s t )(' it ' t ) (9) = ' t + cov(s it ; ' it ); where ' t = 1 n t P nt i=1 ' it is the unweighted rm productivity mean and s t = 1 n t P nt i=1 s it is the mean market share. Note that there is a slight abuse of notation with the de nition of the cov operator, 8

9 which would typically be multiplied by 1=n t. However, since s it s are market shares, they essentially already incorporate the division by the number of rms n t. Ignoring entry and exit of rms, the rst di erence of aggregate productivity index is: = 2 1 = (' 2 ' 1 ) + (cov 2 cov 1 ) = ' + cov; where ' is the change in average productivity and represents the contribution of within- rm productivity improvements, while cov represents the contribution of market-share reallocation. Needless to say, this decomposition only distinguishes between the contributions of productivity improvements and reallocation and thus does not allow us to distinguish between contributions of surviving, entering and exiting rms. However, as we show in the next section, the Olley-Pakes static decomposition of the change in aggregate productivity index can be extended to capture the contributions of these three sets of rms. 3 Dynamic Olley-Pakes decomposition with entry and exit The decomposition that we develop in this section combines two distinct ways of expressing the standard aggregate productivity index. On one hand, the aggregate productivity index can be written as a weighted mean of aggregate productivities of subgroups of rms: t = X g2g s gt gt ; X g2g s gt = 1 where s gt and gt represent the aggregate market share and aggregate productivity of group g in period t: In particular, we shall express aggregate productivities in two subsequent periods as: 1 = s S1 S1 + s X1 X1 ; (10) 2 = s S2 S2 + s E2 E2 ; where S; E and X denote the sets of surviving, entering and exiting rms, respectively. On the other hand, the static Olley-Pakes decomposition can be applied to any group of rms: gt = ' gt + cov gt ; (11) 9

10 where ' gt is the unweighted mean productivity for group g in period t and cov gt is the covariance between market shares and productivity for this group of rms. Using (10) and (11), we rewrite the change in aggregate productivity index as: = ( S2 S1 ) + s E2 ( E2 S2 ) + s X1 ( S1 X1 ) (12) = (' S2 ' S1 ) + (cov S2 cov S1 ) + (13) +s E2 (' E2 ' S2 ) + s E2 (cov E2 cov S2 ) + +s X1 (' S1 ' X1 ) + s X1 (cov S1 cov X1 ): In the rst equality (12), we exploit only the rst feature of the de nition of aggregate productivity (10), which allows us to split the change of aggregate productivity into contributions of surviving, entering and exiting rms. The contribution of surviving rms is positive if aggregate productivity of these rms increases over time. In contrast to Foster et al. (2001) and Griliches and Regev (1995), the contribution of entering rms is positive only if the aggregate productivity of entering rms exceeds the aggregate productivity of surviving rms in period 2, whereas the contribution of exiting rms is positive only if the aggregate productivity of surviving rms exceeds that of exiting rms in period 1. Both of these contributions are weighted by corresponding overall market shares. The second equality (13) exploits also the static Olley-Pakes decomposition and yields six components, two for each set of rms. The interpretations of these components are similar to those in the static Olley-Pakes decomposition. ' S and cov S represent the contributions of productivity improvements and market share reallocations for the subgroup of surviving rms. This misses the contribution of entry and exit to aggregate productivity growth, represented by the other terms. Entrants can contribute to productivity growth in two ways: rst, in a direct way, when their (unweighted) average productivity is higher than that of the surviving rms they compete with (the term s E2 (' E2 ' S2 )); second, in an indirect way, when the covariance between market share and productivity is higher for entrants than for the group of surviving rms (the term s E2 (cov E2 cov S2 )). This is clear in the case where both entrants and the surviving rms have the same unweighted average productivity. If more productive entrants have relatively higher market shares than more productive surviving rms then this positively contributes to an increase in aggregate productivity. One could also consider this channel as a market share reallocation e ect between entrants and surviving rms. Further note that both contributions for the entrants and 10

11 exitors are weighted by their overall market shares, s E2 and s X1, respectively. Exiting rms also contribute to aggregate productivity changes in the same way as entrants: a direct productivity e ect, and an indirect market share reallocation e ect between exiting rms and surviving rms from period 1. From the description of our decomposition is evident that none of the components coincides with those of existing decompositions. The motivating di erence between our decomposition and the decompositions proposed by Griliches and Regev (1995) and Foster et al. (2001) is in the measurement of the contributions of entering and exiting rms. Our decomposition yields positive contribution for entering rms only if aggregate productivity of these rms exceeds the aggregate productivity of surviving rms in period 2, whereas the other two decompositions yield positive contributions for entering rms if aggregate productivity of these rms exceeds either period 1 aggregate productivity of all rms or average of aggregate productivities of all rms in periods 1 and 2. Hence, our decomposition eliminates the inherent bias in the measurement of entering rms when applying Griliches and Regev (1995) and Foster et al. (2001) decompositions. Moreover, as our decomposition yields positive contribution for exiting rms only when their productivity is lower than that of surviving rms in period 1, it also does not su er from the measurement bias of the contribution of exiting rms obtained for Griliches and Regev (1995) decomposition. Use of di erent benchmark productivity indices in calculation of contributions of entering and exiting rms implies that discussed methods yield di erent contributions for surviving rms as well. For the case discussed in Section 2, we would expect that our decomposition gives greater contribution to surviving rms than the other two methods. This is not only a consequence of di erent reference productivity levels, but also due to the fact that the other two methods use lower overall weight for surviving rms. Moreover, our decomposition di ers also in the structure of the contributions of surviving rms. In order to distinguish between the contributions of within- rm productivity improvements from reallocation of market shares between these rms, Griliches and Regev (1995) and Foster et al. (2001) resort to xing weights and/or productivity levels, while we follow Olley and Pakes (1996) and de ne the contributions of the two processes by the changes in distributional moments. These de nitions are clearly di erent and yield di erent contributions of di erent sets of rms. In the latter case, the improvements in productivity index are weighted with xed market shares of rms (that sum to less than 1), whereas in the latter case the changes in productivity index are weighted by equal weights that sum to 1. Thus it is not surprising that the contributions of reallocation of market shares between surviving rms are di erent as well. 11

12 What are the di erences between the contributions of surviving rms in our decomposition and the existing decompositions depends on the actual data sets. In order to give some insight into these di erences, we compare the results of discussed decompositions using real rm-level data. 4 Comparison of decompositions with real data Description of data In comparison of results of di erent decompositions we use the accounting data for a panel of all Slovenian manufacturing rms (NACE 2-digit industries 15-37) for the period data set is well suited for such comparison as during this period the Slovenian economy went through signi cant structural changes. These were triggered by economic reforms in the late 1980s and early 1990s (e.g. liberalization and privatization) and were also re ected in large net entry of rms, fast productivity improvements of surviving rms and signi cant shifts in market shares between di erent sets of rms (see Polanec, 2004). Our data contain information on rm identity, year of reporting, annual sales, material costs, physical capital and employment. From these we calculate all standard measures of labor and total factor productivity. Prior to calculation of productivity measures, we de ate sales and material costs by NACE 2-digit producer price indices and physical capital by investment goods price index. The reported number of employees is calculated from the annual number of hours worked by all workers. Table 1 summarizes the descriptive statistics for the data set of active rms in Slovenian manufacturing. This In order to use the same set of rms in all decompositions, we require that a rm employs at least one worker, engages positive physical capital and generates positive value added. Clearly, this de nition of an active rm is stricter than the legal requirements. The number of rms that comply with our de nition increased by 18.4 percent between 1995 and 2000, from 3,867 to 4,580. Among these rms were 2,677 survivors, 1903 entrants and 1191 exitors. At the same time, the average size of active rms, measured with number of employees, decreased from 60.1 to 45.2 employees, which is mainly a consequence of entry of smaller new rms and partly due to reduction of size of surviving rms. 4 The downsizing of surviving rms and exit of rms also contributed to a decline of aggregate employment by 11.2 percent, from 233 to 207 thousand, despite the fact that 3 We are greatful to the Slovenian Agency for Public Legal Records and Related Services (AJPES) for providing the data. 4 The average employment of surviving rms between 1995 and 2000 declined from 67.4 to 59.4 employees. In 2000, the average employment of entrants was 25.1 employees. 12

13 the real aggregate sales, real aggregate value added and real aggregate physical capital increased by 46.1 percent, 45.8 percent and 25.3 percent, respectively. Table 1: Descriptive statistics for Slovenian manufacturing rms in 1995 and 2000 Year Set of rms Number of all rms Number of survivors Number of entrants 1903 Number of exitors 1191 Variable Average employment Aggregate employment [in thousand] Real aggregate value added [in bln. SIT] Real aggregate output [in bln. SIT] Real aggregate physical capital [in bln. SIT] Notes: The real value added and output are de ated by corresponding. NACE 2-digit industry producer price index. and the real physical capital is de ated by investment goods price index Source: SORS and own calculations. Choice of productivity indices and weights Foster et al. (2001) show that the relative size of di erent components does not depend only on the choice of the method of decomposition, but also on the choice of productivity measure and set of weights. For this reason we compare the results of di erent decompositions using two indices of rm-level productivity with corresponding sets of weights. Since empirical literature frequently used alternative measures of productivity and sets of weights, we rst justify our choice. In what follows, we use two indices of rm-level productivity: log of value added per employee and log of TFP. 5 While log of value added is not a controversial measure of productivity, the measure of productivity obtained from (14) needs further explanation. We calculate it as a residual: ln T F P it = ln Y it ^ ln K it ^ ln Lit ; (14) 5 The productivity indices are given in logs in order to avoid measurement bias when calculating the contributions of surviving rms for our decomposition. If productivity index is not given in logs, the same percentage change in productivity of all surviving rms would be split into equal contributions of the average productivity improvements and the change in covariance of surviving rms. Since all rms improve productivity to the same extent, the contribution of reallocation should be equal to zero, which is achieved when productivity index is given in logs. 13

14 where Y it ; K it and L it denote the real value added, real capital and employment of rm i in period t; respectively, and ^ and ^ denote the estimates of regression coe cients for capital and labor. In order to obtain consistent estimates of log of TFP for the sample of all active rms in the manufacturing sector, the regression equation included both 2-digit NACE industry dummies and annual time dummies. Baily et al. (1992), Foster et al. (2001) and many others estimate the productivity indices using an alternative regression equation with log of sales as the dependent variable and logs of physical capital, employment and material costs as the explanatory variables. This approach is often favored because it does not impose unitary elasticity between sales and material costs. However, Petrin and Levinsohn (2005) show that this measure of productivity is greatly at odds with their measure of welfare (Tornquist-Divisia index) and suggest to obtain the residuals from regression equation given in (14). 6 The second issue related to our estimation of TFP is the choice of estimation method for coe - cients of production function. The ordinary least squares method is known to yield biased estimates of coe cients due to higher average productivity and average size of surviving rms (selection bias) and due to the fact that rms with higher productivity engage greater quantities of production factors (endogeneity bias). In order to reduce these measurement biases, several methods were suggested, although there is still no consensus in the literature regarding the choice of estimation procedure (Add reference e.g. Griliches and Mairesse, 199X). Moreover, these biases vary between di erent samples of rms used in estimation and attempts to eliminate them using alternative estimation methods may have little or no e ect on reduction of bias. Olley and Pakes (1996), who propose a semiparametric estimation method that aims to correct for both selection and endogeneity bias, use a simple test that gives an indication of the magnitude of selection bias. They compare the OLS coe cients for full and balanced samples of U.S. rms producing telecommunications equipment and nd that the coe cient for physical capital is signi cantly lower for the balanced sample. 7 This result leads them to a conclusion that the selection bias a ects the estimates of productivity index. We make a similar comparison for the set of Slovenian manufacturing rms and nd signi cantly lower e ect of selection on the estimated regression coe cients. The 6 In order to check that qualitative di erences between di erent decompositions do not depend on the estimation method for TFP, we have also used TFP obtained from regression of sales on the three production factors. For our data the qualitative di erences carry over to alternative measure of productivity. The results of these estimations are omitted for brevity. 7 Olley and Pakes (1996) estimated the OLS capital coe cient with value added as the dependent variable in a full sample (with entering and exiting rms) and in a balanced sample (only those rms that are active over the entire period). 14

15 coe cient for physical capital estimated for the full sample (0.218) is lower than the same coe - cient estimated for the balanced sample of rms (0.221), whereas the coe cient for employment for the full sample (0.796) is greater than the coe cient for the balanced sample (0.768). A possible reason for lower selection bias may be related to the fact that the key characteristics of rms do not di er signi cantly between the two samples of rms. 8 Insigni cant e ect of selection bias on the estimates of regression coe cients is also re ected in the estimated coe cients of production function using the semiparametric procedures proposed by Olley and Pakes (1996) and Levinsohn and Petrin (2003), which yield decreasing returns to scale and lower coe cient for physical capital than the OLS. For this reason we choose the estimates of rms productivity indices as residuals from the OLS regressions. A related issue is the choice of weights. In the empirical literature it is common to use the weights that correspond to the measure of productivity. We follow this approach and use the employment shares as weights for the log of labor productivity. For the log of TFP we follow Petrin and Levinsohn (2005) and use value added shares as weights. In this way, we look at correspondence between both capital and labor on one hand and TFP on the other hand. 9 It is nevertheless important to note that the main di erences between di erent decompositions are robust to the choice of productivity index and use of alternative weights. Results We now turn to results. As the decomposition proposed by Baily et al. (1992) mismeasures the contributions of entrants and exitors and since the method suggested by Petrin and Levinsohn (2005) decomposes a di erent aggregate productivity index, we only compare the results for our decomposition and the results for the decompositions developed by Foster et al. (2001) and Griliches and Regev (1995). The top panels of Tables 2, 3 and 4 give the results of decompositions for the log of labor productivity, whereas the bottom panels show the decompositions for the log of total factor productivity. The middle columns give the components of decompositions and the last column (denoted total) reports the change of aggregate productivity index. The decompositions are made 8 The full and the balanced sample consist of and observations. The average employment in all years is for the full sample and for the balanced sample of rms. The average of log of value added per employee for the full sample is 7.58 and 7.69 for the balanced sample of rms. 9 Note also that our data show relatively small di erences between the change of our measure of TFP and the Tornquist-Divisia index. The di erence in de nitions between these two indices is that the Tornquist-Divisia index uses corrections for indirect e ects of productivity improvements on other rms in industry, whereas our measure does not. Since we nd small di erences between the two productivity indices, we believe that corrections for indirect e ects are relatively small. 15

16 between 1995 and all subsequent years until 2000 in order to illustrate variation of measurement biases with length of time span. Table 2: Foster, Haltiwanger and Krizan decomposition Log of value added per employee Year Within Between Cross Entry Exit Total Log of total factor productivity Year Within Between Cross Entry Exit Total Notes: The aggregate value added per employee is calculated with employment shares as weights. The aggregate TFP is obtained from regression of log of value added on the log of physical capital and labor using value added as weights. The reference period for calculation of the change of aggregate productivity index is Source: AJPES and own calculations. We rst compare the contributions of surviving, entering and exiting rms for the three decompositions over a ve-year period ( ) using the log of labor productivity as a productivity index. During this period the aggregate productivity index increased by , which can be split in the following ways. The Foster et al. decomposition attributes ( ) to the overall contribution of surviving rms and and to entering and exiting rms, respectively. The Griliches and Regev decomposition attributes a similar contribution to surviving rms, ( ), although the respective contributions of entrants and exitors, and , are quite di erent due to use of a di erent reference aggregate productivity index. Our decomposition yields signi cantly higher overall contribution of surviving rms, ( ), a negative contribution of entering rms, ( ), and an intermediate contribution of exiting rms equal to ( ). These results con rm theoretical predictions about the direction of measurement biases for the 16

17 Table 3: Griliches and Regev decomposition Log of value added per employee Year Within Between Entry Exit Total Log of total factor productivity Year Within Between Entry Exit Total Notes: The aggregate value added per employee is calculated with employment shares as weights. The aggregate TFP is obtained from regression of log of value added on the log of physical capital and labor using value added as weights. The reference period for calculation of the change of aggregate productivity index is Source: AJPES and own calculations. Foster et al. and Griliches and Regev decompositions. Both of these decompositions overestimate the contribution of entering rms and underestimate the contribution of surviving rms, while the Griliches and Regev decomposition trades a part of the upward bias for entering rms for upward bias for exiting rms. Since the Foster et al. decomposition calculates the contribution of exiting rms by comparing their aggregate productivity index to aggregate productivity index of all rms, including exiting rms, it introduces a slight downward bias. Further comparison of results of the decompositions for di erent time periods reveals that the absolute size of measurement biases monotonically increases with length of time span. For example, for the two-year period ( ), the measurement biases for the contributions of surviving, entering and exiting rms for the Foster et al. decomposition are ( ), ( ) and ( ), respectively, whereas for the ve-year period ( ), the corresponding biases are , and Over the two-year period, the biases for surviving, entering and exiting rms for the 10 The relative size of these biases also increases with length of time span. 17

18 Griliches and Regev decomposition are , and and for the ve-year period these are , and , respectively. Note that these results are consistent with the stylized example discussed in Section 2, which suggest that when productivity indices of surviving, entering and exiting rms do not exhibit divergent time trends, the contributions of existing decompositions exhibit increasing measurement biases. 11 Table 4: Dynamic Olley-Pakes decomposition with entry and exit Log of valued added per employee Surviving rms Entering rms Exiting rms Average Average Average Productivity Covariance Productivity Covariance Productivity Covariance Di erence Di erence Di erence Di erence Year Change Change Ent. vs. Sur. Ent. vs. Sur. Sur. vs. Exit. Sur. vs. Exit. Total Log of total factor productivity Surviving rms Entering rms Exiting rms Average Average Average Productivity Covariance Productivity Covariance Productivity Covariance Di erence Di erence Di erence Di erence Year Change Di erence Ent. vs. Surv. Ent. vs. Surv. Surv. vs. Exit. Surv. vs. Exit. Total Notes: The aggregate value added per employee is calculated with employment shares as weights. The aggregate TFP is obtained from regression of log of value added on the log of physical capital and labor using value added as weights. The reference period for calculation of the change of aggregate productivity index is Source: AJPES and own calculations. The qualitative features of observed measurement biases also apply to alternative productivity indices and sets of weights. 12 We illustrate this point for the log of total productivity and shares of 11 The theoretical models of industry dynamics by Jovanovic (1982) and Hopenhayn (1992) imply that entry and exit rates decrease when productivity advantage of surviving rms over entering rms increase and vice versa. The entry and exit rates are stationary only when also when the productivity di erences between surviving, entering and exiting rms are stationary. 12 We have performed robustness checks using alternative sets of weights (sales and employment shares) for two productivity indices: log of TFP obtained from a regression of log of sales on log of capital, labor and material costs and log of TFP obtained from a regression of log value added on log of capital and labor. 18

19 value added as weights in the bottom panels of Tables 2, 3 and For example, over the period the aggregate productivity index increased by The corresponding contributions of surviving, entering and exiting rms for the Foster et al. decomposition are , and , respectively, for the Griliches and Regev decomposition these are , and , whereas for our decomposition these are , and The downward bias for the contribution of surviving rms for the Foster et al. decomposition is , while for the Griliches and Regev decomposition it is On the other hand, the upward bias of the contribution of entering rms for the Foster et al. decomposition is , which is signi cantly larger than for the Griliches and Regev decomposition which yields The Foster et al. decomposition yields small downward bias for the contribution of exiting rms equal to , whereas the Griliches and Regev decomposition yields a large upward bias for exiting rms equal to Thus far we have focused only on how di erent decompositions allocate the change in aggregate productivity index between the contributions of surviving, entering and exiting rms. Since all three methods split the overall contribution of surviving rms between within- rm productivity improvements and reallocation, we can compare the size of these components as well. Looking again at ve-year decompositions for the log of labor productivity, we can see small di erences between the components that capture within- rm productivity improvements, ranging between for the Griliches and Regev decomposition and for the new decomposition. Hence, the downward bias of the contribution of surviving rms for the Foster et al. and Griliches and Regev decompositions is mainly a result of underestimated contribution of reallocation between surviving. That is, our decomposition attributes to reallocation, while the Foster et al. decomposition attributes only ( ) and the Griliches and Regev decomposition attributes This result is, however, not robust to the choice of measure of productivity and set of weights. For the log of TFP with value added shares as weights, we nd that for the ve-year period, the downward bias in the measurement of the contribution of surviving rms for the Foster et al. decomposition results from underestimation of the contribution of within- rm productivity improvements (-0.847= ), whereas for the Griliches and Regev decomposition the bias is mainly a result of underestimation of the contribution of reallocation ( = ). Nevertheless, it is important to note that these di erences in contributions are caused by di erent relative contributions of the Foster et al. decomposition rather than the proposed decomposition. 13 Note that since we calculate the log of TFP as a residual from a regression of the log of value added on the log of capital and labor, the changes of aggregate log of TFP and the contributions of di erent sets of rms are always smaller than the corresponding changes of aggregate log of labor productivity. 19

20 Finally, since only our decomposition splits the contributions of entering and exiting rms into direct and indirect contribution, we describe these results without any comparison. Looking at the Table 4, we nd that the direct contribution of entrants is always negative, irrespective of the choice of productivity index and time span. Since we calculate this component as a weighted di erence between the average productivity of entering and exiting rms, this result implies that entering rms exhibit lower average productivity than the surviving rms. The indirect contribution of entrants is always positive for the log of total factor productivity and mixed for the log of labor productivity, but always relatively small, which suggests that there are small di erences between covariance of entering and surviving rms. The direct contribution of exitors is the largest single component for both productivity indices. A large positive value for this term implies that the exiting rms had lower productivity than the surviving rms and thereby contribute to higher aggregate productivity. Moreover, the direct contribution of exiting rms increases with length of time span. 14 On the other hand, the indirect contribution of exiting rms is always negative, which implies greater covariance between size and productivity for exiting rms than for surviving rms. 5 Sectoral dynamic Olley-Pakes decomposition with entry and exit The proposed decomposition given in (13) can be applied at any level of industrial aggregation of rms, moreover, the components of decomposition at higher level of aggregation can be expressed in terms of components at the lower level of aggregation. In this section, we derive the expressions for the components of decomposition at the sectoral level in terms of the components of decompositions at industry level under the assumption that rms do not shift their focus of market activity and remain in the same industry over time. By assuming this we eliminate a channel of inter-industry reallocation. 15 However, even in this simpli ed case the components of decomposition at the level of sector that capture reallocation can not be expressed as simple weighted averages of industrylevel components, but rather as a sum of two sets of components re ecting intra and inter-industry market reallocations. Starting from the expression for the sectoral level decomposition (13) and preserving the notation, we can express the sectoral components in the following way. The component that captures the productivity improvements of surviving rms is the only one that can be expressed as a simple 14 The variation of size of components with length of time span is further discussed in Appendix. 15 The share of rms that change the focus of economic activity is relatively small and the bias due to this type of inter-industry reallocation is small as well. 20