Cross-Country Differences in Productivity: The Role of Allocation and Selection

Cross-Country Differences in Productivity: The Role of Allocation and Selection Eric Bartelsman, John Haltiwanger & Stefano Scarpetta American Economic Review (2013) Presented by Beatriz González January 2016 Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and Selection 2016 1 / 21

Outline 1 Motivation 2 Harmonized Indicators of Dispersion and Covariance 3 The Model 4 Allocation and Selection in Heterogeneous Firm Model 5 Calibration 6 Results 7 Robustness checks 8 Conclusions Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and Selection 2016 2 / 21

Motivation Two facts 1 There are large and persistent differences in productivity across countries. 2 There is large and persistent heterogeneity in firm-level productivity. Several papers combine these two facts: Relate differences in economic outcomes to within-productivity dispersion across firms. Examples: Restuccia and Rogerson (2008), Hsieh and Klenow (2009), Midrigan and Xu (2008). Which measures of firm-level heterogeneity are most instructive for detecting possible misallocation? Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and Selection 2016 3 / 21

Motivation Evidence in firm-level data: Distribution of productivity and size exhibit positive correlation. Variation in the strenght of correlation across countries, industries and over time. Evidence of misallocation: Use variety of moments drawn from the data. Focus on allocation of resources across firms AND selection of firms. Hypothesis: Policy-induced distortions are the source of the covariance variation Helps explaining differences in aggregate performance Data: Harmonized firm-level database from US and Europe, including Central and Eastern Europe. Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and Selection 2016 4 / 21

Motivation Contribution Study firm-level size-productivity relationship in an heterogenous firm model. 1 Within-industry covariance bewteen size and productivity is a robust measure to assess the impact of misallocation. 2 Match different moments across countries using distortions to revenue. Size/productivity relationship varies significantly among countries: stronger in more advanced economies. Within-industry dispersion in labor productivity is larger than that of total factor productivity. Assess the extent to which distortions can account for the observed differences across countries and over time in the within-industry productivity dispersion. Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and Selection 2016 5 / 21

Preliminaries 1 Revenue Labor Productivity (LPR), computed in the data as revenue per worker. LPR si = P siy si L si 2 Revenue Total Factor Productivity (TFPR): P siy si TFPR si = K αs si L 1 αs si 3 Physical Total Factor Productivity (TFPQ): TFPQ si = Y si K αs si L 1 αs si 4 Olley-Pakes decomposition (1996). Index of the productivity of an industry. Ω s = i θ is ω is = ω s + (θ is θ s )(ω is ω s ) i }{{} OP covariance Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and Selection 2016 6 / 21 (1)

Harmonized Indicators of Dispersion and Covariance Within-Industry Productivity Dispersion and OP Covariance Term Three basics moments are used in this paper:std(lpr), STD(TFPR) and OP. VOL. 103 NO. 1 BARTELSMAN ET AL.: CROSS-COUNTRY DIFFERENCES IN PRODUCTIVITY 311 Table 1 Within-Industry Productivity Dispersion and OP Covariance Term (Weighted averages of industry-level data, US industry weights) STD in revenue labor productivity STD in revenue total factor productivity OP covariance term United States 0.58 0.39 0.51 United Kingdom 0.59 0.42 0.15 Germany 0.71 NA 0.28 France 0.53 0.23 0.24 Netherlands 0.55 0.15 0.30 Hungary 1.04 0.92 0.16 Romania 1.05 0.55 0.03 Slovenia 0.80 0.22 0.04 Notes: Averages over 1993 2001 data. Industry-level firm based TFP measures not available for Germany. Source: Firm-level database; see Bartelsman, Haltiwanger, and Scarpetta (2009). It is also instructive to explore the within-country variation over time of these moments. These moments are available for a number of years spanning the period 1992 2001 (except for France, where data are available through 1995). Table 2 Presented by Beatriz presents González the within-country (UC3M) Cross-Country changes Differences in the moments in Productivity: comparing The the Roleaverage of Allocation for January the and Selection 2016 7 / 21

Harmonized Indicators of Dispersion and Covariance Within-Industry Productivity Dispersion and OP Covariance Term Main takeaways: 1 STD(LPR) and STD(TFPR) is large in all countries. 2 For all countries, STD(LPR) > STD(TFPR) holds. 3 OP term is positive for most of the countries, and exhibits systematic cross-country patterns. Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and Selection 2016 8 / 21

Harmonized Indicators of Dispersion and Covariance Within-Country Variation Over Time 312 THE AMERICAN ECONOMIC REVIEW FEBRUARY 2013 Table 2 Changes in Productivity Dispersion and OP Covariance Term (Weighted averages of industry-level data, US industry weights) STD in revenue labor productivity STD in revenue total factor productivity OP covariance term United States 0.02 0.00 0.09 United Kingdom 0.04 0.03 0.06 Germany 0.06 NA 0.14 France NA NA NA Netherlands 0.01 0.00 0.11 Hungary 0.02 0.03 0.18 Romania 0.03 0.03 0.25 Slovenia 0.06 0.02 0.16 Notes: Change is difference in moments between the average value in 1997 2001 and the average value in 1993 1996. Data for France available only from 1992 to 1995 and for the United States for 1992 and 1997. Source: Firm-level database; see Bartelsman, Haltiwanger, and Scarpetta (2009). Main takeaways: model is developed to capture an important fact observed in the data in all countries: the dispersion in revenue labor productivity within industries exceeds the dispersion in revenue total factor productivity, even in economies with few or no distortions. To match this feature of the data, we include quasi-fixed capital in the presence of transitory productivity shocks and overhead labor. 1 OP covariance term increased substantially in the transition economies over time. 2 Dispersion measures are relatively stable over time. A. The Model Presented by BeatrizStarting González with (UC3M) the behavior Cross-Country of firms, Differences we assume in Productivity: that firms produce The Role of according Allocation January to and a Selection 2016 9 / 21

The Model Production of the heterogeneous units: decreasing returns to scale. Y it = A i ɛ it (n it f ) γ α k α it, γ < 1 (2) Perfectly competitive final good aggregator The implied inverse demand is ( ) 1 ρ 1 ρ Y t = Nt Y ρ ρ it i ( ) 1 Ȳt ρ P it = P t Y it Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 10 / 21

The Model Firms maximize π it = (1 τ i κ it )P t Ȳ t 1 ρ [ Ai ɛ it (n it f ) γ α k α it ] ρ wt n it R t k it (3) Overhead labor f Quasi-fixed capital (from timing of the shocks). Entry: Ex-ante: only know G(A, τ). The free entry condition is: W e = max (0, W (A, τ)) dg(a, τ) c e (4) A,τ Ex-post: pay ce, draw A i, τ i G(A, τ) that will remain constant over the life of the firm. W (A i, τ i ) = E [π(a i, τ i, κ it, ɛ it )] ( ) 0 (5) 1 1 λ 1+r Exit if can t cover their costs Only the surviving subset M(A, τ) stays. Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 11 / 21

The Model Timing of incumbents Decide whether to produce or not, based on F (ɛ) and H(κ). Choose kit Learn draws of ɛ it and κ it Choose l it = (n it f ) Face exogenous death probability λ. Given k it, labor choice depends upon realization of transitory shocks. For each firm, expected profits are the same in every period. Main drawbacks of this framework: Capital stock is fixed over the firms life cycle. Exit is exogenous after the decision to produce has been made. Absence of business cycles or growth. Household problem. Equilibrium Conditions. Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 12 / 21

Allocation and Selection in Heterogeneous Firm Model Allocation With Cobb-Douglas technology and constant wage rate, equalization of average revenue product of labor. In absence of distortions, firms with highest TFPQ will have higher output and input. In the absence of distortions, LPR is increasing in firm size Positive OP covariance Overhead labor (f ) LPR i = P iy i n i = P i Y i (n i f ) + f LPR are positively correlated with TFPQ. Selection Leads to misallocation! Highly productive firms (high A i ) with bad distortion (high τ i ) will exit. Low productivity firms are able to operate. Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 13 / 21

Calibration US as a non-distorted economy ( τ i, κ it ): choose parameters to match US moments. Empirical evidence in literature: γ = 0.95, α = 0.3, γ = 0.10, ρ = 0.8 Use f, c e and variances of A i, ɛ it to match exactly survival rate (55%) and one of the moments of table 1 ( choose OP covariance). Properties of the benchmark: Overhead labor plays a critical role. 322 THE AMERICAN ECONOMIC REVIEW FEBRUARY 2013 1.10 1.00 US Benchmark 0.90 0.80 0.70 STD(LPR) STD(TFPR) COV(LPR) Survival 0.60 0.50 0.40 0.30 0.20 0.10 0.20 0.06 0.10 0.14 0.18 Overhead costs Figure 1. The Impact of Overhead Costs on Key Moments is suggested by another key pattern in Figure 1 that is, the share of entering firms that survive declines monotonically with overhead labor costs. Eventually overhead labor costs become sufficiently high that much of the distribution of firms is cut off by selection, and this yields a decline in the covariance. Similarly, the standard Presented by Beatriz González (UC3M) deviation Cross-Country of LPR, while also initially Differences rising sharply in with Productivity: overhead labor, eventually The Role of Allocation January and2016 Selection 14 / 21

Calibration Calibrated benchmark economy is able to capture features of the data: High dispersion of revenue based measures of total factor and labor productivity. Greater dispersion in labor productivity than in total factor productivity. Large OP covariance between size and productivity. High failure rate among entrants (45% of failure in first 5 years) What next? Using distortions alone (τ i, κ it ), try matching cross-country variation of key moments. Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 15 / 21

Impact of Correlated Distortions Allow distortions to be positively correlated to idosyncratic productivity draw Rationale: Existence of corruption, preferential treatment. Set correlation at 0.95, vary the dispersion of distortions. 324 THE AMERICAN ECONOMIC REVIEW FEBRUARY 2013 0.8 The relationship between productivity dispersion and distortion dispersion 1 The relationship between OP covariance moments and distortion dispersion 0.7 0.6 0.5 STD(TFPR) STD(LPR) 0.4 0 0.50 1.00 1.50 2.00 2.50 Distortion dispersion 0.8 0.6 0.4 0.2 0 0 0.50 1.00 1.50 2.00 2.50 0.2 Distortion dispersion COV(LPR) COV(TFPR) COV(TFPQ) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 The relationship between selection, entry costs, and distortion dispersion Survival fraction Entry cost/output 0 0.50 1.00 1.50 2.00 2.50 Distortion dispersion 1.2 1.1 1 0.9 0.8 0.7 The relationship between key aggregate indices and distortion dispersion Consumption index K/L index 0 0.50 1.00 1.50 2.00 2.50 Distortion dispersion Figure 3. The Relationship between Key Moments and Outcomes with Distortion Dispersion ( Positive correlation case) reported in Figure 2. Over the range of the horizontal axis in Figure 2, the ratio of Impact of Uncorrelated dispersion Distortions of distorted to nondistorted profit shocks ranges from 1 to 2. Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 16 / 21

Matching Observed Moments Try to match different moments in tables 1 and 2 by distortions alone Hard job because of non-monotonic relationship! 326 THE AMERICAN ECONOMIC REVIEW FEBRUARY 2013 Match OP covariance exactly. Country Table 3 Key Data Moments and Model Moments when the Model is Calibrated to Match the OP LPR Covariance COV_LPR (Data) COV_LPR (Model) STD_LPR (Data) STD_LPR (Model) STD_TFPR (Data) STD_TFPR (Model) Consumption Index (Model) United States 0.51 0.51 0.58 0.75 0.39 0.47 1.00 United Kingdom 0.15 0.15 0.59 0.66 0.42 0.69 0.93 Germany 0.28 0.28 0.71 0.59 NA 0.64 0.97 France 0.24 0.24 0.53 0.60 0.23 0.66 0.96 Netherlands 0.30 0.30 0.55 0.59 0.15 0.63 0.97 Hungary 0.16 0.16 1.04 0.65 0.92 0.69 0.93 Romania 0.03 0.03 1.05 0.72 0.55 0.70 0.88 Slovenia 0.04 0.04 0.80 0.70 0.22 0.70 0.89 is much greater if the distortions are positively correlated with productivity. This makes intuitive sense as distortions in this case have a greater bite insofar as they not only add noise but actively induce the most productive firms to stay smaller and the least productive firms to survive and be larger than would have been the case in a distortion-free environment. Presented by Beatriz González (UC3M) Cross-Country C. Matching Differences the Observed in Productivity: MomentsThe Role of Allocation January and2016 Selection 17 / 21

Robustness checks Lower Overhead Labor Overhead labor has an effect on endogenous selection. Set it sufficiently small so that all firms produce in the absence of distortions. Match STD(TFPR) in the US. 328 THE AMERICAN ECONOMIC REVIEW FEBRUARY 2013 1.2 1 0.8 0.6 0.4 0.2 0 0 0.5 1 1.5 2 2.5 0.2 STD(TFPR) STD(LPR) COV(TFPQ) Survival COV(LPR) 0.4 Distortion dispersion Figure 4. The Impact of Distortion Dispersion on Key Moments (Low overhead case) Cannot match STD(LPR) > STD(TFPR)! with low overhead labor, although the pattern is somewhat more complex for LPR. For TFPQ, we find that the covariance between size and productivity falls monotonically with distortion dispersion. For LPR, the covariance first increases over Presented by Beatriz González some range (UC3M) and then Cross-Country declines. The Differences increasing inportion Productivity: reflects The the fact Rolethat of Allocation in the January and2016 Selection 18 / 21

Robustness checks Measurement Error Assess the potential impact of measurement error on results: Introduce a multiplicative measurement error in revenue How does it affect COV(LPR) and STD(TFPR)? VOL. 103 NO. 1 BARTELSMAN ET AL.: CROSS-COUNTRY DIFFERENCES IN PRODUCTIVITY 329 1.4 1.2 1 COV(LPR) STD(TFPR) 0.8 0.6 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Measurement error Figure 5. The Impact of Measurement Error on Dispersion of TFPR and Covariance (LPR) Introducing a multiplicative measurement error in employment has in revenue that is classical does not change the measured covariance between LPR and employment. This follows from the property that the expectation of the product substantial effect of uncorrelated on both variables variables. is the product of the expectations. However, in unreported results we show that multiplicative measurement error in employment has a substantial impact (UC3M) on both Cross-Country dispersion Differences and the covariance. in Productivity: The effect The on Role the covariance of Allocation January and2016 Selection 19 / Presented by Beatriz González 21

Robustness checks Dispersion in Factor Elasticity of Labor Low overhead labor, no distortions, dispersion in factor elasticities Obtain dispersion in LPR Not feasible to match US moments OP covariance falls STD(LPR) < STD(TFPR) Negative Correlation between Distortions and Productivity Would this increase allocative efficiency? Do model simulations allowing for negative correlation between distortions and productivity. Increase in prductivity/size covariance Increase in consumption. Changing degree of dispersion or the negative correlation yields non-monotonic results Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 20 / 21

Conclusion Allocation and selection interact in complex ways with firm-heterogeneity, frictions, and distortions to yield aggregates. First to consider size-productivity relationship in this class of frameworks. Closely related, stronger in more advanced economies Within industry dispersion in labor productivity is larger than that of total factor productivity. Size-productivity realtionship is more robust to measurement errors. Benchmark of US: heterogeneous firms facing frictions (overhead labor and quasi-fixed capital) and idiosyncratic productivity shock. Overhead labor is trivial in matching key patterns in non-distorted benchmark and on selection. Changing the distribution of distortions alone (τ i, κ it ) match cross-country variation of key moments. Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 21 / 21

Appendix Household Problem Household Households supply N t of labor inelastically. max {c} s.t. β t U(C t ) t=0 p t (C t + K t+1 (1 δ)k t ) = t=0 This gives us Back p t (w t N t + R t K t + π t ) (6) t=0 r t = R t δ = (1/β) 1 (7) Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 22 / 21

Appendix Market Clearing Conditions Free entry condition Labor Market Clearing Final Good Market Clearing W e = 0 N d t = N s t C t + E t c e + δk t = Y t Back Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 23 / 21

Appendix ImpactVOL. of Uncorrelated 103 NO. 1 Bartelsman Distortions et al.: Cross-Country Differences in Productivity 323 The relationship between productivity The relationship between OP covariance dispersion and distortion dispersion moments and distortion dispersion 0.8 0.55 COV(LPR) COV(TFPR) 0.95 0.7 0.5 COV(TFPQ) (right axis) 0.45 0.90 0.85 0.6 STD(TFPR) STD(LPR) 0.5 0.4 0.4 0.35 0.3 0.80 0.75 0.70 1.00 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 0.20 0.40 0.60 0.80 Distortion dispersion Distortion dispersion The relationship between selection, entry costs, and distortion dispersion 0.60 0.50 Survival fraction Entry cost/output 0.40 0.30 0.20 0.10 0 0 0.20 0.40 0.60 0.80 1.00 Distortion dispersion The relationship between key aggregate indices and distortion dispersion 1.20 1.10 1.00 0.90 0.80 Consumption index K/L index 0.70 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Distortion dispersion Figure 2. The Relationship between Key Moments and Outcomes with Distortion Dispersion (Uncorrelated case) Back firms, with an accompanying increase in the cost of entry as a share of output, an increase in the capital-labor ratio, and a decline in consumption. Both the capital- Presented by Beatriz González (UC3M) Cross-Country Differences in Productivity: The Role of Allocation January and2016 Selection 24 / 21