Determinants of Efficiency of Law Firms

Presenter: EunYoung Whang

Coauthors: Rajiv Banker, Marina Angel

Temple University

July 11, 2009

Organizational Changes

• During last three decades, law firms have changed dramatically

• Total number of lawyer have more than tripled in 2008 compared to 1984 (AmLaw 100)

• Transition from “boutique” law firms to “megafirms” that provides specialized and full-line legal services globally

• Expansion of partnership structure from one-tier to multi-tier partnership

Megafirms• Some law firms have grown• To provide full line of legal service in different

specializations • To have more resources to attract big corpo-

rate and institutional clients• To expand geographical reach, especially in

international market

Multi-Tier Partnerships • Adopted to retain and motivate talented lawyers

with more promotion opportunities• One-tier partnership law firms have only equity

partners• Two-tier partnership law firms have both equity

and non-equity partners• Only 20% of AmLaw 100 firms have one-tier part-

nership in 2008, down from 55% in 1994• Number of non-equity partners is increasing at a

faster rate than equity partners and may have di-luted the “rain-making” intensity of senior partners

Lawyer Leverage

• Unlike manufacturing firms, law firms assets are human capital resources; equity part-ners, non-equity partners, and lawyers

• More lawyers per partners leverages the tal-ent and ability of partners

• Very high span-of-control may affect ability to manage effectively

Apparent Contradictions?

• Baker & McKenzie ranked first by the number of lawyers but ranked 98 out of 100 firms in terms of revenue per lawyer(RPL)(AmLaw 100, 2008)

• Wachtell, Lipton, Rosen & Katz ranked last in terms of the number of lawyers but ranked first in terms of RPL (AmLaw 100, 2008)

Hypotheses

• Hypothesis 1: The size of law firms is posi-tively related to productivity

• Hypothesis 2: The proportion of non-equity partners has a negative relationship with productivity

• Hypothesis 3: Higher leverage (lawyers : partners ratios) is associated with higher productivity

Two-Stage DEA Analysis• Banker & Natarajan (2008) prove the estima-

tor is consistent• 1st stage: Estimate efficiency score with DEA • 2nd stage: Regress efficiency score on contex-

tual variables• Recent Monte Carlo evidence shows this

simple approach outperforms the bootstrap approach

Data

• AmLaw 100 dataset provides for human capi-tal resource and financial data

• Sample period: 2000~2007• Sample size: 648 firm-year observations

(81 law firms * 8 years)

Human Resources Inputs• Equity partners

- highest job title (most highly compensated)

- have ownership (share profit & loss)

- rainmaker and most productive personnel • Non-equity partners

- intermediate step to become equity partner

- paid fixed salary (do not share profit & loss)• Lawyers

- do most of legal work in law firm

- paid fixed salary (do not share profit & loss)

Output Variable

• Gross revenue: fee income generated from legal work

• Deflated by Consumer Price Index(CPI)

DEA Estimation Models• Technical Efficiency:

Banker, Charnes and Cooper (BCC) (1984)

• Aggregated Efficiency: Charnes, Cooper and Rhodes(CCR)(1978, 1981)

• Scale Efficiency

= CCR Efficiency/BCC Efficiency• Estimated (1) year-by-year, (2) pooled

Efficiency Trends from Pooled Estimation

2000 2001 2002 2003 2004 2005 2006 20070

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Cross section efficiency(BCC)Pooled efficiency(BCC)Cross section efficiency(CCR)Pooled efficiency(CCR)

Test of Returns to Scale

Null Hypothe-ses

Alternative Hypotheses

Test Result

CRS VRS Rejected

NDRS VRS Supported

NIRS VRS Rejected

CRS NDRS Rejected

CRS NIRS Supported

Returns to Scale Inference

CRS

IRS

X0

Y

Second Stage ModelLog(θ) = f{Size, %Non-equity partners,

Leverage, Control Variables}• Control variables:

- Regional firm

- International firm

- Geographic regions

- Post-merger

- Year trend(for pooled analysis)

Variable MeasurementSize (+) = # of lawyers+# of partners

%non-eq-uity part-ners

= # of non-equity partners/# of equity partners

Leverage = # of lawyers/# of equity partners

Regional =1 have no more than 45% of firm’s attorneys were located in any one region of the country, =0 o/w

Interna-tional

=1 more than 40% of lawyers located outside US, =0 o/w

Post-merge =1 for post merger years

Northeast =1 if headquarter location is in New York, Philadelphia, Pittsburg, or Boston

West =1 if headquarter location is in San Francisco, Los Angeles, Seattle or Palo Alto

Midwest =1 if headquarter location is in Chicago, St. Louis, Milwaukee, Kansas City, Cleveland, or Minneapolis

Dealing with Panel Data

• Fama-McBeth Regressions: year-by-year cross-sectional model

• Prais-Winsten Regression: pooled efficiency

Fama-MacBeth Regression Results

Hypo.Sign

BCC CCR

Intercept -0.587*** -0.772***

Size + 0.0001*** -0.000006

%non-equity partner

_ -0.131*** -0.119***

Leverage + 0.078*** 0.118***

Prais-Winsten Regression Results

Hypo. Sign

BCC CCR

Intercept -0.674*** -0.898***

Size + 0.0001*** -0.000006

%non-equity partner

_ -0.132*** -0.118***

Leverage + 0.083*** 0.123***

Robustness Check• One stage parametric production func-

tions with contextual variables

- Translog function

- Cobb-Douglas function• Same control variables as in the DEA

models

Parametric Function Results

Predicted Sign

Translog Model

Cobb-Dou-glas Model

Size + -0.0003 -0.0003**

%non-eq-uity part-ner

_ 0.004 -0.012

Leverage + 0.041 0.041

Conclusion• Organizational changes have resulted in pro-

ductivity improvement in law firms during 2000 – 2007

• Technical efficiency (BCC) increases with

- the size of law firm- smaller proportion of non-equity partners- the degree of leverage