structural change in the job matching process before the great … · 1 structural change in the...

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Structural change in the job matching process before the Great Contraction in the United States, 1924 – 1932

Woong Lee*à

Korea Institute for International Economic Policy (KIEP) 246 Yangjaedaero, Seocho-gu, Seoul, 137-747, Korea

Abstract This paper examines a possibility of structural changes before the Stock Market Crash of 1929 in the job matching process operated by public employment offices in the United States. The data are drawn from public employment offices, a labor market intermediary that links job-seekers and employers, whose major clients were low skilled, migrants and immigrants. To detect structural breaks, the Andrews-Quant and the Bai-Perron structural breakpoint tests are employed. The results show that a structural change was detected about a year before the Stock Market Crash, which suggest that the sign of the depression was detected in the public labor exchange when the economy was in the period of rapid economic expansion. JEL classification: J23; J49; J63; N32. Key Words: Labor Market – U.S., 1920s, Great Depression; Matching Function; Public Employment Offices; Structural Changes.

{It is very first draft. Please do not cite.}

* All the errors and views in the paper are the author’s own. à Fax: 822-3460-1044. Email address: [email protected] or [email protected].

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1. Introduction

It is generally viewed that the Stock Market Crash of 1929 ignited the Great Depression in the

United States. Although the Stock Market Crash is a good guess, there is no clear evidence that

the most severe recession in the U.S. history, including the labor market, came immediately in

the late 1929. In fact, the U.S. economy seemed to be in downturn before the Stock Market

Crash (Blanchard 2003). Dornbusch and Fischer (1984) also argue that real out began to drop

before the Stock Market Crash.1

This paper examines whether there were structural changes in the labor exchange market

before the Great Contraction, the period between the late 1929 and 1933. A matching function

approach is utilized to explore a possibility of downturn in the labor market before the Stock

Market Crash of 1929.

The matching function is a simple way to introduce frictions that cause transaction costs

in the labor market. Because of imperfect information and exchange frictions between job-

seekers and employers, new hires do not occur instantaneously between the agents. Hence, time-

consuming searching and finding for both sides are required and the existence of these

transaction costs in job matching is outlined by a matching function. In the matching function

framework, the job matching process is described by the joint movement of job seekers and

vacant jobs. Like aggregate production function such that production is a function of capital and

labor, matches (new hires) are a function of job-seekers and vacancies.

The matching function is a widely used in macro-labor literature and many researchers

have estimated matching functions for various countries or markets (Petrongolo and Pissarides

2001). In the U.S. case, Blanchard and Diamond (1990), Bleakley and Fuhrer (1997), and

1 It is re-citation in Romer (1990), p. 597.

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Borowczyk-Martins, Jolivet and Postel-Vinay (mimeo) estimated the U.S. matching functions.

Blanchard and Diamond results using 1970s’ data show that the elasticities for unemployment

and job vacancies are 0.42, 0.62 respectively, and the matching functions exhibit constant returns

to scale. Bleakley and Fuhrer’s estimates for the period from 1979 to 1993 are 0.64 for

unemployment and 0.36 for vacancies and constant returns to scales cannot be rejected. With the

assumption of constant returns to scale, Borowczyk-Martins, Jolivet and Postel-Vinay show that

the elasticities of the matching function with respect to job-seekers and vacancies are 0.18 to

0.32 and 0.68 to 0.82, respectively.

The data on job-seekers, vacancies and new hires are collected from public

employment offices, a non-profit government organization to match job-seekers and employers.

Major clients of public employment offices were low skilled workers, unskilled workers (casual

workers, common laborers, and service workers), immigrants, or migrants in the early 20th

century (Lee, 2009). The role of public employment offices was influential to the U.S. labor

market, starting from the U.S. involvement with the World War I. Evidence shows that

approximately 5 percent or higher of the U.S. labor force utilized public employment offices

since 1920s (Lee 2009).

To examine structural changes in the matching function, the Andrew-Quant structural

break tests for one unknown breakpoint (Andrews 1993) and the Bai-Perron unknown multiple

breakpoint test are performed. The results show that there was a structural break in July or

August 1928, which suggests that the job matching process conducted by the U.S. public

employment offices revealed a sign of downturn one year before the Stock Market Crash.

Before the break, the contributions of job-seekers and vacancies to create new hires were

approximately 0.2 and 0.8 respectively, which indicates that the role of job vacancies was more

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important in creating new hires through public employment offices. After the break, the role of

job-seekers in job matching vanished and the matching process became entirely vacancy-driven:

the estimate for job-seekers is zero and the one for job vacancies is one. This change implies that

unfavorable labor market conditions for job-seekers in the public labor exchange were

exacerbated one year before the Great Contraction.

Therefore, at least in the labor exchange service operated by public employment offices

in the United States, a downturn began about one year before the onset of the Stock Market

Crash and the estimates of structural break support this possibility. This finding suggests that a

sign of the depression was seen when American economy was in the period of economic boom in

the 1920s.

This paper is organized as follows. Section 2 introduces main labor market indicators as

well as economy-wide measures for business cycle to check a possibility of downturn before the

Wall Street Panic of 1929. Section 3 presents an overview of the matching function. Section 4

introduces a brief outline of the U.S. public employment offices and its data used in this paper.

Section 5 reports results of estimating matching functions and structural break tests and Section 6

concludes the paper.

2. The U.S. Labor Market during the 1920s and the 1930s.

This section summarizes trends of the U.S. labor market in the 1920s and the 1930s with

key economic indicators. Before introducing labor market variables, two important measures

precede in order to see overall variation of business cycle in this period.

Figure 1 presents quarterly trends of the U.S. GNP and Industrial Production Index (IPI)

from 1921 to 1939. The GNP is gross national product and IPI is a measure for the real

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production output of manufacturing, mining, and utilities. 2 IPI is a monthly series but for

comparison reason, March, June, September, and December values are selected in Figure 1.

Firstly, it looks obvious that the U.S. economy was in boom in the 1920s before late 1929. GNP

grew more than 70 percent from 1921 to 1929 but dropped sharply aftermath of the Stock Market

Crash of 1929. GNP recovered its 1929 level around the end of 1936. The Industrial Production

reveals similar pattern of GNP in the 1920s and 1930s, confirming a huge downturn in the late

1929. These two macro variables related to production indicate that the Great Depression,

especially the Great Contraction3, started with the Stock Market Crash. However, in its actual

monthly series, IPI was at peak in July 1929 and started to decrease from August 1929, two

months earlier than the Wall Street Crash.

Figure 2 displays various estimates of the unemployment rate in the 1920s and the 1930s.

These values indicate a similar implication as GNP and IPI. The estimates look stable in the

1920s except the 1921 recession. The unemployment rate soared in 1930 and sharply increased

to more than 20 percent at peak and did not lower below 10 percent in the 1930s. Unfortunately,

data for the unemployment rate are annual series thus unlike GNP and IPI cannot precisely

provide the sign of downturn before the Stock Market Crash.

Figure 3 illustrates the U.S. Manufacturing Employment Index from January 1921 to

June 1936. It is originally produced by the National Industrial Conference Board and published

in Beney (1936). It is made using comprehensive monthly survey of approximately 1.5 million

workers hired in the 25 industries in the U.S. manufacturing sector. This index is commonly used

to explore the early 20th labor market in the U.S. (e.g., Bernanke 1986). As most of the data

2 - The Industrial Production Index (IPI) is an economic index published by the Federal Reserve Board of the U.S., measuring the real production output of manufacturing, mining, and utilities. It provides monthly, seasonally adjusted estimates with the base year of 2007 (http://research.stlouisfed.org/fred2/help-faq). 3 It means the severe recession from late 1929 to 1933, leading to the Great Depression.

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shown, the manufacturing employment index also shows the similar pattern, especially

substantial drop starting in the late 1929. Like IPI, however, it was at the maximum in June 1929

and began to decline in July 1929, i.e. before the Stock Market Crash of October 1929.

Figure 4 provides the Help Wanted Advertising Index (HWI) which is a measure of

relative level of labor demand. It is based on the median monthly percentage changes in the

number of help-wanted advertisements published in the U.S. newspapers (Boschan 1966).

Berridge (1929) invented this monthly index for the Metropolitan Life Insurance Company,

spanning from January 1919 to August 1960. The usefulness of this index is supported by

Boschan (1966), which states that HWI conformed perfectly to business cycle of the U.S.

economy during the period of 1920s up to the early 1960s. HWI also reveals a considerable

reduction in the late 1929 but shows different patterns from other indicators. HWI looks more

volatile and is more sensitive to seasonal factors. Its values in the 1920s display more seasonal

fluctuation than those in the 1930s. Unlike GNP, IPI, and HWI shows that a shortage of labor

demand was prolonged and its recovery was slow.

Figure 5 shows both nominal and real average hourly wages (AHW) in the U.S.

manufacturing sector between January 1926 and June 1936. Unlike other previously expressed

variables, both series were stable in the 1920s. A distinction is that nominal AHW began to

decline in the middle of 1930 but real AHW showed upward trend since 1925. The gap between

these two series was the largest in 1933, when the U.S. economy was in the most severe

recession. This large gap between the two was mainly due to serious deflation during the period

of the Great Contraction. An interesting point is that real AHW became higher than nominal one

from January 1930, which might implies a sign of recession in the economy. Hence trends of

AHW could possibly be considered as an indication of entering depression of the U.S. economy

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before the Wall Street Crash of October 1929.

In summary, although most of economic indicators on the labor market show the late

1929 is the starting point where the U.S. economy entered into the trap of the Great Depression,

these measures turning point such as IPI (from August 1929), the manufacturing employment

index (from July 1929), AHW (from January 1929) tends to precede October 1929, the month of

the Stock Market Crash.

3. Matching Functions

The coexistence of unemployed and vacant jobs can be explained by frictions in the job

matching process. The matching function is widely used in literature to introduce frictions that

cause transaction costs in the labor market (Pronongo and Pissarides 2001). In the matching

function, the joint movement of job-seekers and vacancies describe the job matching process

with properties as follow:

(1) = ( , )

(2)

> 0,

> 0

(3) (0, ) = 0, ( , 0) = 0

(4) < 0, < 0

Equation (1) is a general form of the matching function. M represents the number of

matches (hires) in a given time interval, U the number of job-seekers, and V the number of job

vacancies. Equation (2) shows that the matches increase with respect to an increase in the

number of job-seekers job vacancies. Equation (3) indicates that at least one job-seeker and one

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job vacancy are required to generate a match. Equations (2) and (4) imply the concavity of the

matching function. Two additional requirements are introduced to formulate the matching

function. The one is that S equals the number of the unemployed (Cahuc and Zylberberg 2004).

The other is that constant returns to scale is assumed in search-matching models go generate

stable and unique equilibrium of the unemployment (Pissarides 2000).

This paper uses a Cobb-Douglas representation of the matching function shown in

Equation (5). It is a generally used functional form for the matching function in literature. Other

functional forms can also be considered such as translog or CES (constant elasticity of

substitution) but empirical evidence supports Cobb-Douglas specification (Pronongo and

Pissarides 2001).

(5) = ( , ) =

where = ∙ ( + )

Here t represents time frequency. All the variables are indexed by t because the data used in this

paper are time series. By taking logarithm of both sides in Equation (5), the Cobb-Douglas

representation is transformed to be linear in parameters:

(6) = + + + + where log A = c

The α is interpreted as the elasticity of the matching function with respect to job-seekers and is

the elasticity with respect to job vacancies.4 Loosely speaking, α is the percentage change in M

with respect to one percent increase in S.

4 can be often interpreted as additional effects in the efficiency of the matching process over time. Mathematically,

=

= ̇ ⁄ .

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The degree of returns to scale for the matching function is obtained by the sum of α and β

and can be tested under the null hypothesis: α + β = 1 in (5) or (6). The α and β are also

considered as the relative importance or contributions, or the matching shares of job-seekers and

vacancies to create new job matches. Following Petrongolo and Pissarides (2001), the matching

function is assumed to be constant returns to scale and Equations (5) and (6) are re-shaped to

Equations (7) and (8) respectively:

(7)

=

(8)

= + (1 − ) + +

The

is the job finding rate for workers, the number of matches divided by the

number of job-seekers, is called the labor market tightness,

, and is the elasticity for job-

seekers. Labor market tightness is a proxy for excess labor demand. It can be said that the labor

market is tight or slack if

> 1 or

< 1. However,

= 1 does not indicate balanced labor

exchange, which means that labor market conditions for job-seekers and firms are equally likely.

This only measures relative labor demand. Thus it can be said that a labor market is tight if

employers have trouble in filling vacant jobs or need a long wait to fill an available job. In

contrast, tighter labor market or higher labor market tightness is in favor of finding a job for

workers.

In this paper, the key interest is to test whether the matching function coefficients show

structural change in response to the Stock Market Crash of October 1929. If the Stock Market

Crash initiated the substantial downturn of the labor market, then the job matching process

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showed structural break after 1929. This issue is explored in Section 6 after introducing the data

drawn from public employment offices to estimate matching functions in the 1920s and the early

1930s.

4. Data from the U.S. Public Employment Offices

Background of Public Employment Offices

Public employment offices (PEOs hereafter) are non-profit governmental organizations

matching job-seekers and employers. As a labor market intermediary, one of its main purposes is

to reduce job search costs for both sides in order to improve job-seekers’ finding a job and

employers’ filling a vacant job. Introducing PEOs is a type of government interventions to

prevent market failure or inefficiency where other labor market institutions such as informal

networks or private employment agencies do not work properly.

PEOs began to be introduced in the late 19th century and it was a widespread

phenomenon in Western world (US Employment Service 1935). In the United States, since the

first five PEOs were established in Ohio in 1890, PEOs’ role was minimal until 1920s except the

period of World War I (Lee 2009). The role of PEOs was sizable in the 1920s. The usage of

PEOs by job-seekers in the 1920s was approximately 5 to 6 percent of the total labor force it

reached more than 20 percent in 1939 (see Table 1). PEOs’ impact was substantial in the 1930s

when the U.S. government initiated relief programs including unemployment compensation for

the recovery. PEOs also made more than one million of job placements each year in this period,

as shown in Table 1. PEOs’ performance was at the highest in 1933 when almost 7 million

placements were made.

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In summary, PEOs’ position in the U.S. labor market was not important in the first two

decades of the 20th century but its role grew substantially over time. Eventually PEOs became a

major labor market intermediary since 1920s and its role was especially influential for recovery

in the 1930s.

Data

The data used in this paper are drawn from PEOs in the U.S. in the 1920s and 1930s.

Three key variables are the number of job-seekers, vacancies and new matches. These are time

series data and the frequency is month. The range is from July 1923 to January 1932 and hence

total observation is 103.

The data are collected from “A Monthly Report of Activities of State and Municipal

Employment Services Cooperating with United States Employment Services” published by the

U.S. Employment Service (1924 – 1932).

“Registrations” is used for the number of job-seekers, “Help Wanted” for the number of

job vacancies, and “Placed” for the number of new hires. “Registrations” is the sum of the

number of new applicants who are registered to look for a job in a month and existing applicants

who did not find a job in the previous period thus renewed their registrations in a month. “Help

Wanted” represents the number of job positions requested by employers to public employment

offices in a month. “Placed” is the number of applicants who were hired when referred to

employers, with PEOs requiring evidence of engagement before recording a placement (Stewart

and Stewart 1933).

“Registrations”, “Help Wanted” and “Placed” drawn from PEOs are suitable for the main

variables of the matching function. In current literature, many researchers have adopted the data

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from public employment offices to estimate matching functions (e.g., Cole and Smith 1996 for

the Britain; Yashiv 2000 for Israel; Kano and Ohta 2005 for Japan).

The data from PEOs are useful because a non-trivial number of job-seekers, about 5

percent in a year, utilized PEOs in this period, as shown in Table 1. In addition, this data set is

the only source to estimate matching functions in the United States in the 1920s and 1930s. Its

usefulness

The practicality of data is supported by a contemporary scholar, William A. Berridge

(1926) who utilized the data in the six states’ offices: Pennsylvania, New York, Massachusetts,

Ohio, Illinois, and Wisconsin. He constructed “office ratio” which is equivalent to the labor

market tightness, “the ratio of jobs offered by employers to jobs applied by work-people at the

public employment offices” to examine the relationship between voluntary quits and movement

of the labor market in the 1920s (page 138). He stated that the data from PEOs were constructed

in well-organized methods for public job matching and long records of statistical data were

collected in a reliable and constant way.

One important point to be noticed on the data in PEOs is its representativeness. Although

all types of workers used PEOs but its major clients were low skilled workers, unskilled workers

(casual workers, common laborers, and service workers), immigrants, or migrants (Lee, 2009).

However, some of workers categorized as semi-skilled or skilled were actually unskilled in the

early 20th century, implying that actual portion of unskilled workers was higher than the one

recorded in the Census (Goldin 2000). In addition, the data from PEOs are especially useful for

the 1930s because the majority of unemployed workers during the Great Depression were low

skilled (Margo 1993). Thus, the data from PEOs are less biased than expected.

The other point, which is less noticeable, to be concerned is the composition of the

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number of job-seekers. In PEOs’ data, the number of job-seekers includes on-the-job search and

unemployed workers. In the matching function framework, unemployed workers represent job-

seekers. In this case, using job-seekers instead of the unemployed has an advantage because

actual frictions in the labor exchange are caused by the interactions among all job-seekers

including on the job search. This issue is not important because most job-seekers registered in

PEOs in the early 20th century were unemployed (Stewart and Stewart 1933).

Before performing regression analyses, trends of main variables constructed from the

data set are provided in Figures 6 and 7. Figure 6 shows trends of job-seekers (U), vacancies (V),

and new matches (M) from July 1923 to January 1932. It indicates that the number of job-seekers

was higher than that of job vacancies and this gap became larger in the late 1929. Co-movement

of job vacancies and new matches are also observed. An interesting aspect is that the number of

job-seekers was relatively stable but job vacancies and new hires substantially dropped with the

onset of the Great Contraction. These trends may suggest that job matching process through

PEOs was exacerbated mainly due to a sharp drop in vacant jobs in the early stage of the Great

Depression.

Figure 7 presents the labor market tightness, the ratio of the number of job vacancies to

the number of job-seekers. Its trend looks similar to job vacancies and new matches. Thus it is

inferred that a substantial drop in the labor market tightness around the late 1929 was due to

sharp decline in job vacancies. Another observation is that the labor market tightness was always

less than one in this period, which implies that there was excess labor supply for unskilled

workers and this unfavorable condition worsened with the onset of the Great Depression.

Trends of the PEOs’ data also illustrate that the U.S. labor market’s downturn point was

late 1929 although it looks a couple of months earlier than the Stock Market Crash of October or

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November 1929. Tests whether the job matching process shows earlier structural change than

October 1929 are performed in the next section.

5. Empirical Works

This section estimates matching functions with the data drawn from PEOs and performs

structural break tests to evaluate whether the job matching process in the U.S. public labor

exchange had structural change in response to the Stock market Crash of the late 1929.

Before performing regression analyses, since all variables are time-series monthly data,

stationarity of each variable is tested and the results are shown in Table 2. All variables are in

natural logarithm form following the regression specifications in Equations (6) and (8). Here m is

log(M), u is log(U), v is log(V), f is log(M/U) and vu is log(V/U). SA in parenthesis means

seasonally adjusted series. The results of ADF (Augmented Dickey-Fuller) test indicates that m,

u, and v with or without seasonal adjustment are stationary but f and vu without seasonal

adjustment barely passed the unit root test at 10 percent level of significance. Moreover, after

seasonal adjusted, f and vu tend to follow a unit root process.5 Thus, tests for cointegration of f

and vu without and with seasonal adjustment are performed. EG-ADF test statistics in Table 2

are the results from a cointegration test. EG-ADF (Engle-Granger Augmented Dickey-Fuller)

statistics prove that the regressions of f and vu before and after seasonal adjustment are

cointegrating, implying that the relationship between f and vu is not spurious but economically

valid.6 Therefore, estimation of the matching function specified in Equations (6) and (8) do

5 The ADF examines if a variable follows a unit root process. The null hypothesis is that the variable follows a unit root process and the alternative is that the variable is stationary (Stata Press 2009, p. 117). In ADF test, you can have options to include constant or constant and trend. You can also include lagged values of the difference of the regression specification. 6 The EG-ADF test is used when the coefficient in the regression is unknown. In this paper’s case, first estimation is performed for Equation (8). Next a Dickey-Fuller test is implemented for the residual from the step and check if the

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provide meaningful economic relationships.

Table 3 presents the results from estimating matching functions using Equation (6), a

general form of the matching function. Newey in columns [1] and [3] provides the results from

OLS regression with Newey-West HAC (heteroskedasticity- and autocorrelation-consistent)

standard errors for coefficients (Stock and Watson 2006, pp. 606-608).7 Prais in columns [2] and

[4] represents Prais–Winsten and Cochrane–Orcutt regression (Stata Press 2009, p. 237). Prais

uses feasible generalized least square (FGLS) method to estimate coefficients in a linear

specification, like Equations [6] or [8], where errors are autocorrelated (Greene 2003, pp.273-

276). In both Newey and Prais, various lag length options for the dependent variable are tested

and the estimation results are robust on the lag length. Columns [1] and [2] are the estimates with

no seasonally adjusted variables and [3] and [4] are the ones with seasonal adjustment of the

variables. The main finding in Table 3 is that the job matching process was vacant-job dependent.

The estimates for job vacancies (V) are more than 0.9 while the coefficients for job-seekers (U)

are between 0.06 and 0.08. These findings confirm the co-movement of job vacancies and new

matches in Figure 6, which implies that job vacancies’ contribution to create new job matches

was the most and the role of job-seekers was minimal in the labor exchange operated by PEOs.8

Tests for returns to scale show that matching functions exhibit constant returns to scale

(CRS). In all specifications, this result is robust: α + β is approximately one through [1], [2], [3]

and [4] and the null hypothesis of CRS cannot be rejected in all cases as shown in Table 3.

Following CRS results, matching functions are re-estimated using Equation (8) and the

results are presented in Table 4. Same methods, Newey and Prais, are applied for estimating CRS

residual is stationary or not (Stock and Watson 2006, p. 659). 7 “The error structure is assumed to be heteroskedastic and possibly autocorrelated up to some lag.” (Stata Press 2009, p. 217). 8 Implication of the estimates of matching functions is not the main issue in this paper. Regarding this issue, see Lee (mimeo).

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matching functions. The estimates for vu, that is 1 – α in Equation (8), are compared to the

estimates for V in Equation (6). The results with CRS assumption in Table 4 are consistent with

the ones without CRS in Table 3. The estimates for 1 – α are between 0.91 and 0.94 and this

shows the same implication in Table 3.

Before implementing structural break tests, time aggregation bias should concerned in

estimating matching functions (Petrongolo and Pissarides 2001). In the matching function

structure, this bias arises because the dependent variable, M, is a flow variable (value in a time

interval) and the control variables, U and V, are stock variables (values at a point in time). In

general, Data for the number of matches are documented in a given period (e.g., in a month,

quarter, or year) but the number of job-seekers and vacancies are recorded at the end of the

period. In this case, the stock of U and V are decreased by the flow of new matches, which

causes a downward bias in estimating matching functions. However, this problem is not applied

in this paper because all variables constructed with PEOs data are flow variables, including

values in a month. This means that the volumes of job-seekers and vacancies are not reduced by

new matches, which indicates no downward bias in the estimates of matching function.

Therefore all variables in the matching function estimation are contemporaneously timed.

One more concern is the representativeness that is already mentioned in the previous

section. The data from PEOs are biased toward low and skilled workers and thus the estimates of

matching function with PEOs data do not represent the population. Thus, the results in this paper

are representative for the subsample of the population, job-seekers who used the labor exchange

market operated by PEOs.9

9 Although it is not representative of the population, Lee (mimeo) estimates matching functions in the 1920s and 1930s with the use of industry-occupation level data for Illinois and New York states. To correct the bias toward unskilled workers, the population distribution is used for sampling weights in the estimation of matching functions. Interestingly, the results with and without the sampling weights are almost same, suggesting the same implication.

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Table 5 presents the results from an unknown structural break test, the Andrew-Quandt

structural break (AQ) test. The AQ test is designed by Andrews (1993) and Andrews and Ploberger

(1994) to test an unknown structural breakpoint for a regression model in a sample. The sup F- or

Maximum F-statistics is the maximum of individual Chow F-statistics. The AQ test picks the point where

produces the highest Chow F-statistic with the critical values calculated by Andrews (1993), which are

different from the critical values of Chow F statistic. The idea is that a single Chow test is performed at

every observation within trimmed data (QMS 2009, pp. 172-173). Next, test if each point is a breakpoint

using Chow test F statistics. Lastly, among the Chow F statistics that passed the null of a breakpoint, the

maximum value of F-statistics is chosen. In Table 5, Maximum F stat is the maximum of the individual

Chow F-statistics.10 The AQ test suggests the structural breakpoint in August 1928, 14 months before the

Stock Market Crash. This finding indicates that the job matching process started being exacerbated a year

before the onset of the Great Contraction.

More rigorous tests for structural changes are performed. The AQ test determines only

one breakpoint but this may not be the case. Thus the Bai-Perron unknown multiple breakpoint

test (BP test hereafter) is adopted to find structural changes in the job matching function,

Equation (8), (Bai and Perron 1998, 2003).11 The procedures of the BP test is that first minimum

segment length, in proportion to data is defined. It is equivalent to trimmed data in the AQ test.

Given this restriction, the optimal partition of all possible segments is searched in order to find

global minimums of the sum of squared residuals. Finding global minimums provides the

location of structural breaks for any possible number of breaks. Finally, the breakpoints are

sequentially tested for whether an additional breakpoint significantly reduces the sum of squared

errors.

Bai and Perron (1998, 2003) use three main tests to determine breakpoints. The first test

10 In this paper, the AQ test for a single unknown breakpoint is performed using Eviews. 11 This paper performed the BP test by implementing Professor Perron’s Gauss code posted on his homepage (- http://people.bu.edu/perron/code.html)

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is Sup FT(B, q) test for the null hypothesis of no structural change against the alternative of a

fixed number of changes.12 The second is the UD max and WD max tests. UD test is named as

double maximization test. Its null hypothesis is no structural break against the alternative of an

unknown number of breaks given some upper bound, B. WD max test “applies weights to the

individual tests such that the marginal p-values are equal across values of” the maximum

number of breaks allowed” (Bai and Perron 2003, p. 14). The last one is the Sup FT(l|l+i) test.

This test is a sequential test of the null hypothesis of l breaks against the alternative of (l+i)

breaks. In addition, there are BIC and LWZ tests to select the number of breaks.13

This paper performs the BP tests based on Equation (8), the matching function with CRS.

Ten specifications are considered in the BP tests: the cases of one to five breaks with and without

seasonal adjustment of the variables in the matching function. Table 6 summarizes the results of

the BP tests in all ten cases. When the variables with no seasonal adjustment are used, two

breakpoints are detected: July 1928 and August 1930. Here July 1928 is very close to the

breakpoint suggested by the AQ test in Table 5. When only one break is allowed, the BP test

chooses July 1928. This implies that the job matching process through PEOs began to change in

the middle of 1928, about one year earlier than the beginning of the Great Contraction. The other

breakpoint, August 1930 may suggest further downturn in the labor market after the Great

Depression hit the U.S. economy. After seasonal adjustment of the variables, the BP test

determines three breakpoints: July 1928, July 1926 and October 1924. In the case of seasonally

adjusted variables, when one breakpoint is allowed in estimation, July 1928 is selected by the BP

test. October 1924 can possibly be interpreted as a sign from 1924 depression but July 1926 as a

12 B is maximum number of breaks allowed and q is the number of regressors whose coefficients are allowed to change (http://people.bu.edu/perron/code.html) 13 BIC represents Bayesian Information Criterion and LWZ stands for a modified Schwarz criterion (Bai and Perron 2003, p. 17).

19

structural change is not easy to be inferred.

Lastly, assuming the matching technologies were different before and after July 1928, the

top candidate selected by the BP test, matching functions are estimated separately for the period

from July 1923 to June 1928 and the period after July 1928 and the results are shown in Table 7.

The estimates with and without seasonal adjustment are almost identical. Before the structural

break, matching functions’ coefficients are approximately 0.8, which indicate that the

contribution of job vacancies is about 80 percent to generate new hires or one percent increase in

job vacancies causes 0.8 percent increase in new job matches. Although the job matching process

is still vacancy-driven, the contribution of job-seekers, about 0.2, is not trivial before the

structural change. However, after the break, the estimate increases to one, implying that the job

matching process becomes entirely vacancy-dependent. There is no contribution of job-seekers

for new matches. The drop in job-seekers’ importance from 0.2 to zero is substantial. Therefore,

it can be inferred that unfavorable labor market conditions for job-seekers in the labor exchange

through PEOs were aggravated more than one year before the Great Contraction.

6. Conclusion

This paper assessed the job matching process by estimating matching functions in the

1920s and the early stage of the Great Depression with the data drawn from public employment

offices in the United States. Tests for structural break were performed to examine whether the

matching function parameters changed in response to the Stock Market Crash of the late 1929.

The findings suggest that at least in the labor exchange service operated by the U.S public

employment offices, a structural break was detected about one year before the beginning of the

Great Contraction that was initiated by the Wall Street Crash of 1929. Therefore, it is suggested

20

that in some markets, the sign of the Great Contraction was detected when the U.S. economy was

in the period of rapid economic expansion.

References Andrews, D. W. K. Tests for parameter instability and structural change with unknown change

point. Econometrica, 61:821–856, 1993. Andrews, D. W. K. and Ploberger, W. Optimal tests when a nuisance parameter is present only

under the alternative. Econometrica, 62:1383–1414, 1994. Bai, J. and P. Perron (1998), "Estimating and Testing Linear Models with Multiple Structural

Changes," Econometrica, 66, 47-78. Bai, J, and P. Perron (2003), "Computation and Analysis of Multiple Structural Change Models,"

Journal of Applied Econometrics, 18, 1-22. Beney, A.M. Wages, Hours, and Employment in the United States, 1914-1936, National

Industrial Conference Board, New York, 1936. Berridge, William A. “Labor and the Business Cycle: Some Industrial Aspects.” Review of

Economics and Statistics 8, no. 3 (1926): 134-43. Berridge, W.A. Labor turnover in American factories, Monthly Labor Review 29, no.1 (1929)

62−65. Blanchard, O. J. and Diamond, Peter A, The Aggregate Matching Function, in Growth,

Productivity and Unemployment. Peter A. Diamond, ed. Cambridge: MIT Press, pp. 159- 206. 1990.

Bleakley, Hoyt and Fuhrer, Jeffrey C. Shifts in the Beveridge Curve, Job Matching, and Labor Market Dynamics. New England Economic Review 9:10 (1997) pp. 3-19.

Borowczyk-Martins, Daniel, Jolivet, Gregory and Postel-Vinay, Fabien. New Estimates of the Matching Function, mimeo

Boschan, C. Job Openings and Help-Wanted Advertising as Measures of Cyclical Fluctuations in Unfilled Demand for Labor. In The Measurement and Interpretation of Job Vacancies. NBER. the Columbia University Press, New York, 1966, pp. 489-518.

Bernanke, B.S. Employment, hours, and earnings in the depression: an analysis of eight manufacturing Industries, American Economic Review 76, no.1 (1986) 82−109.

Cahuc, P. and Zylberberg, A. Labor Economics, first ed., MIT Press, Cambridge, 2004. Coles, Melvyn G. and Smith, Eric. “Cross-Section Estimation of the Matching Function:

Evidence from England and Wales.” Economica 63, no. 252 (1996): 589-97. Dornbusch, R. and Fischer, S. Macroeconomics, 3rd Edition. New York: McGraw Hill, 1984. Goldin, Claudia. “Labor Markets in the Twenties Century.” In the Cambridge Economic History

of the United States, III, edited by Stanley L. Engerman and Robert E. Gallman, 549-624. New York: Cambridge University Press, 2000.

Greene, W. Econometric Analysis, fifth ed., Prentice Hall, Upper Saddle River NJ, 2002. Kano, Shigeki and Ohta, Makoto. “Estimating a Matching Function and Regional Matching

Efficiencies: Japanese Panel Data for 1973-1999.” Japan and the World Economy 17 (2005): 25-41.

Lee, W. Private deception and the rise of public employment offices in the United States,

21

1890−1930, in D. Autor (ed.), Studies of Labor Market Intermediation, University of Chicago Press, Chicago, 2009, pp. 155-181.

Lee, W. Slack and Slacker: Job-Seekers, Job Vacancies, and Matching Functions in the U.S. Labor Market during the Roaring Twenties and the Great Contraction, 1924-1932, mimeo.

Margo, Robert. “Employment and Unemployment in the 1930s.” Journal of Economic Perspective 7, no. 2 (1993): 41-59.

Petrongolo, B. and Pissarides, C. A. 2001. Looking into the Black Box: A Survey of the Matching Function, Journal of Economic Literature 39, no. 2 (2001) 390-431.

Pissarides, C.A. Equilibrium Unemployment Theory, second ed., MIT Press, Cambridge, 2000. Quantitative Micro Software (QMS), LLC. Eviews 7 User’s Guide II, 2009 Romer, C. Spurious volatility in historical unemployment data, Journal of Political Economy 94,

no.1 (1986) 1-37. Romer, C.D., The Great Crash and the Onset of the Great Depression, Quarterly Journal of

Economics 105, no. 3 (1990): 597-624.. Smiley, G. Recent unemployment rate estimates for the 1920s and 1930s, Journal of Economic

History 43, no.2 (1983) 487-493. Stata Press, Stata Time Series Reference Manual Release 11. 2009. Stock, J.H. and Watson, M.W. Introduction to Econometrics, second ed., Pearson-Addison-

Wesley, Boston, 2006. Stewart, A. M., and Stewart, B. M. Statistical Procedure of Public Employment Offices, New

York: Russell Sage Foundation. 1933. US Employment Service, Monthly Report of Activities of State and Municipal Employment

Services Cooperating with U.S. Employment Service, Jan. 1924 – Jan. 1932. Washington, DC: Government Printing Office.

US Employment Service. 1935, Historical Sketch of Public Employment. Employment Service News 2, No. 2 (February): 2–8.

US Employment Service. September 1934 – December 1940. Employment Service News, No. 1 – 7, No. 12 Washington, DC: Government Printing Office.

US Employment Service. 1935b. Twelve and One-Half Millions Registered for Work 1934. Washington DC: Government Printing Office.

Wier, D. R, A Century of U.S. Unemployment, 1890 – 1990, Research in Economic History 14, (1992) 301-346.

Yashiv, Earn. “The Determinants of Equilibrium Unemployment.” American Economic Review 90, no.5 (2000): 1297-332.

Data Sources (Internet)

NBER Macrohistory Database: - http://www.nber.org/databases/macrohistory/contents/index.html Federal Reserve Economic Data (FRED), St. Louis Fed: - http://research.stlouisfed.org/fred2 - http://research.stlouisfed.org/fred2/help-faq Pierre Perron's Homepage - http://people.bu.edu/perron/code.html

22

Figures

Figure 1: U.S. GNP and Industrial Production Index, 1921Q11 – 1939Q4

Source: - GNP (NBER Macrohistory Database), http://www.nber.org/databases/macrohistory/contents/index.html - Industrial Production Index (Federal Reserve Economic Data, St. Louis Fed), http://research.stlouisfed.org/fred2 Note: - The GNP is gross national product in constant dollars. It is quarterly and seasonally adjusted. Its unit is billions of 1939 dollars. - The Industrial Production Index (IPI) is an economic index published by the Federal Reserve Board of the U.S., measuring the real production output of manufacturing, mining, and utilities. It provides monthly, seasonally adjusted estimates with the base year of 2007 (http://research.stlouisfed.org/fred2/help-faq). - To compare with GNP, values of March, June, September, and December in the Industrial Production Index are taken from the original series. - Left axis is for GNP and right one for IPI.

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Figure 2: Unemployment Rates in the 1920s and 1930s

Source: Lebergott – BLS and Coen (Smiley 1983, p. 488); Romer (Romer 1986, p. 31); Wier (Wier 1992, pp. 341 – 342)

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Figure 3: Index of the U.S. Manufacturing Employment, 1921:1 – 1936:6

Source: employment (Beney 1936); Note: - It is an index of the U.S. manufacturing sector that made with monthly survey of 1.5 million workers hired in the 25 representative industries in the manufacturing sector in the early 20th century. - The Base for the index is the 1923 average.

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Figure 4: Help Wanted Advertising Index (HWI)

Source: NBER Macrohistory Database. Note: - HWI (SA) is seasonally adjusted series. - HWI’s base is 1945 – 1947 average = 100 - HWI is a measure of relative level of labor demand. It is based on the median monthly percentage changes in the number of job vacancy advertisements published in newspapers (Boschan 1966). Berridge (1929) created this monthly national help-wanted index for the Metropolitan Life Insurance Company, spanning from January 1919 to August 1960. - Trend of the HWI conformed perfectly to business cycle of the U.S. economy during the period of 1920s up to the early 1960s except the postwar boom of 1945 - 1948 and its coverage is more restricted to professionals, white-collar, and skilled workers (Boschan 1966)

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Figure 6: Job-Seekers, Vacancies, and Matches through the U.S. Public Employment Offices, 1923:7 – 1932:1

Source: U.S. Employment Service 1924 – 1932

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Figure 7: Labor Market Tightness, 1923:7 – 1932:1

Source: U.S. Employment Service 1924 – 1932 Note: - θ represents the labor market tightness, the ratio of the number of vacant jobs to the number of job-seekers.

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Tables

Table 1: Performance of the U.S. Public Employment Offices in 1920s and 1930s

Sources: 1923-1930 (U.S. Employment Service, 1924-1931); 1933 (U.S. Employment Service 1935); 1934-1940 (U.S. Employment Service, 1934-1940). Note: - U is the number of job-seekers who utilized public employment offices. - M is the number of job placements made by public employment offices. - LF stands for total labor force.

year U M U as a % of LF

1923 2755593 1806990 6.34%

1924 2663846 1609977 6.02%

1925 2727763 1791381 6.04%

1926 2440640 1688476 5.35%

1927 2259095 1412645 4.87%

1928 2332505 1534092 4.95%

1929 2346316 1345936 4.91%

1930 2421936 1104136 4.99%

1931

1932

1933 12634974 6951523 24.83%

1934 4111000 2821893 7.96%

1935 5980463 5188096 11.44%

1936 3858926 4224387 7.28%

1937 6539589 2896890 12.16%

1938 8090370 3125183 14.84%

1939 12873531 3524949 23.31%

30

Table 2: Unit Root and Cointegration Tests

Note: - An augmented Dickey-Fuller (ADF) test is performed for stationarity with no lagged difference. - The Engle-Granger ADF (EG-ADF) test is adopted to check cointegration for f and vu. - The null hypothesis for ADF test is that the variable shows a unit root. - The null hypothesis for EG-ADF test is no cointegration in the variables. - * indicates 1 percent of level of significance, ** 5 percent, and *** 1 percent.

constant constant and trend

m -4.165*** -5.013***

u -7.066*** -7.446***

v -3.898** -4.900***

f -2.681* -3.277*

vu -2.515 -3.266*

m (sa) -3.177** -4.498***

u (sa) -5.643*** -6.421***

v (sa) -2.931** -4.300***

f (sa) -1.946 -2.069

vu (sa) -1.888 -2.059

ADF Test StatisticEG-ADF test statisticSeries

-5.960***

-5.685***

31

Table 3: Matching Function Results

Note: - Newey represents OLS Regression with Newey-West standard errors. - Prais is FGLS estimation with Cochrane-Orcutt AR(1) regression using iteration. - For Newey, all results are robust with respect to lag lengths of the dependent variable. - For Prais, various AR structures of the dependent variable are tested and AR(1) to correct serial correlation and AR(1) is chosen.

dependent variable = m

[1] [2] [3] [4]

Newey Prais Newey Prais

constant -0.238 -0.258 -0.092 -0.181

(0.274) (0.167) (0.285) (0.168)u 0.078*** 0.060** 0.071*** 0.069***

(0.021) (0.027) (0.023) (0.020)v 0.924*** 0.943*** 0.920*** 0.930***

(0.013) (0.018) (0.014) (0.015)t 0.001*** 0.001*** 0.001*** 0.001***

(0.000) (0.000) (0.000) (0.000)

month dummies Yes Yes No No

(adjusted) R2 0.996 0.992

obs 103 103 103 103

AR(1) 0.598 0.506

D-W statistic (transformed) 2.025 1.963

CRS Yes Yes Yes Yes

Not seasonally adjusted Seasonally adjusted

Control Variables

32

Table 4: Matching Function Results - Constant Returns to Scale Assumed

Note: - Newey represents OLS Regression with Newey-West standard errors. - Prais is FGLS estimation with Cochrane-Orcutt AR(1) regression using iteration. - For Newey, all results are robust with respect to lag lengths of the dependent variable. - For Prais, various AR structures of the dependent variable are tested and AR(1) to correct serial correlation and AR(1) is chosen.

dependent variable = f

Newey Prais Newey Prais

constant -0.229*** -0.226*** -0.201*** -0.203

(0.008) (0.008) (0.004) (0.007)

vu 0.924*** 0.943*** 0.924*** 0.905***

(0.012) (0.018) (0.012) (0.014)

t 0.001*** 0.001*** 0.001*** 0.001***

(0.000) (0.000) (0.000) (0.000)


(adjusted) R2 0.987 0.980

obs 103 103 103 103

AR(1) 0.599 0.519

D-W statistic (transformed) 2.022 1.783

Control VariablesNot seasonally adjusted Seasonally adjusted

33

Table 5: Andrews-Quandt (one) Unknown Breakpoint Test

Note: - Null Hypothesis is no breakpoints within trimmed data. - Equation Sample ranges from July 1923 to January 1932. - Test Sample after trimming is between November 1924 and September 1930 (71 observations).

Seasonal adjustment

Statistic Value p-value Value p-value

Maximum LR F-statistic (1928M08) 21.646 0.000 53.176 0.000

Maximum Wald F-statistic (1928M08) 21.646 0.000 53.176 0.000

no yes

34

Table 6: Summary of the Bai-Perron Unknown (Multiple) Breakpoint tests

Note: * indicates 1 percent of level of significance, ** 5 percent, and *** 1 percent.

B = 1 1928:7*** 1928:7**

B = 2 1928:7*** 1930:8*** 1928:7** 1926:7**

B = 3 1928:7*** 1930:8*** 1928:7*** 1926:7** 1924:10**

B = 4 1928:7*** 1930:8*** 1928:7*** 1926:7** 1924:10**

B = 5 1928:7*** 1930:8*** 1928:7** 1926:7** 1924:10**

no seasonal adjustment seasonal adjustment

35

Table 7: Matching Functions: before and after the breakpoint, July 1928

Note: * indicates 1 percent of level of significance, ** 5 percent, and *** 1 percent.

dependent variable = f

1923:7 - 1928:6 1928:7 - 1932:1 1923:7 - 1928:6 1928:7 - 1932:1

constant -0.244*** -0.311*** -0.241*** -0.270***

(0.006) (0.022) (0.006) (0.019)

vu 0.813*** 1.007*** 0.804*** 1.006***

(0.023) (0.020) (0.020) (0.019)t 0.001*** 0.002*** 0.001*** 0.002***

(0.000) (0.000) (0.000) (0.000)


(adjusted) R2 0.980 0.996 0.960 0.995

obs 43 60 60 43

AR(1) 0.357 0.162 0.293 0.140

D-W statistic (transformed) 2.119 1.854 2.113 1.898

(1-α) = 1 No Yes No Yes

Control VariablesNot seasonally adjusted Seasonally adjusted

36

Appendix A.1: Descriptive Statistics

Note: m = log(M); u = log(U), v = log(V); f = log(M/U); vu = log(V/U). A.2: Bai-Perron Structural Change Test with No Seasonal Adjustment and B = 1

Note: - zt is the matrix of regressors whose coefficients are allowed to change. - q is the number of regressors whose coefficients are allowed to change. - p is the number of regressiors with coefficients being fixed across regimes. - h is minimal length of segment. - B is maximum number of structural changes allowed. - Sup FT(B) is the test statistic for the test with the null hypothesis of no structural change against the alternative of a fixed number of changes. - UD max is the statistic for the test with the null of no structural break against the alternative of an unknown number of breaks given an upper bound, B. - WD max is the statistic for weighted UD max test. - Sequential is the sequential test performed in the Bai-Perron structural change test. - BIC represents Bayesian Information Criterion and LWZ stands for a modified Schwarz criterion to detect the number of breakpoints.

Variable Obs Mean Std. Dev. Min Max

m 103 11.712 0.256 11.185 12.293

u 103 12.240 0.136 11.928 12.574

v 103 11.850 0.284 11.292 12.525

f 103 -0.528 0.187 -0.939 -0.211

vu 103 -0.390 0.216 -0.842 0.027

zt = {1} q = 1 p = 13 h = 15 B = 1

SupFT(1) UDmax WDmax

13.458*** 13.458*** 13.458**

Sequential 1

LWZ 1

BIS 1

T1

1928:7***

(1927:9-1929:11)

Specifications

Tests

Number of breaks selected

Estimates of the breakpoints

37

A.3: Bai-Perron Structural Change Test with No Seasonal Adjustment and B = 2

Note: - Sup FT(l|l+i) is the test statistic for a sequential test with the null hypothesis of l breaks against the alternative of (l+i) breaks. - For others, see A.2. A.4: Bai-Perron Structural Change Test with No Seasonal Adjustment and B = 3

Note: see A.2 and A.3

zt = {1} q = 1 p = 13 h = 15 B = 2

SupFT(1) SupFT(2) UDmax WDmax SupFT(2|1)

13.458*** 13.501*** 13.501*** 15.314*** 29.399***

Sequential 2

LWZ 1

BIS 1

T1 T2

1928:7*** 1930:3***

(1928:5-1930:2) NA

Specifications

Tests



zt = {1} q = 1 p = 13 h = 15 B = 3

SupFT(1) SupFT(2) SupFT(3) UDmax WDmax SupFT(2|1) SupFT(3|2)

13.458*** 13.501*** 10.603*** 13.501*** 17.727*** 29.399*** 29.399***

Sequential 2

LWZ 1

BIS 1

T1 T2

1928:7*** 1930:8***

(1928:5-1930:2) NA

Specifications

Tests



38

A.5: Bai-Perron Structural Change Test with No Seasonal Adjustment and B = 4.

Note: see A.2 and A.3 A.6: Bai-Perron Structural Change Test with No Seasonal Adjustment and B = 5.


zt = {1} q = 1 p = 13 h = 15 B = 4

SupFT(1) SupFT(2) SupFT(3) SupFT(4) UDmax WDmax SupFT(2|1)

13.458*** 13.501*** 10.603*** 9.078*** 13.501*** 18.025*** 29.399***

SupFT(3|2) SupFT(4|3)

29.399*** 0.872

Sequential 2

LWZ 1

BIS 1

T1 T2

1928:7*** 1930:8***

(1928:5-1930:2) NA

Specifications

Tests



zt = {1} q = 1 p = 13 h = 15 B = 5

SupFT(1) SupFT(2) SupFT(3) SupFT(4) SupFT(5) UDmax WDmax

13.458*** 13.501*** 10.603*** 9.078*** 9.504*** 13.501*** 23.788***

SupFT(2|1) SupFT(3|2) SupFT(4|3) SupFT(5|4)

29.399*** 29.399*** 0.872 0.000

Sequential 2

LWZ 1

BIS 1

T1 T2

1928:7*** 1930:8***

(1928:5-1930:2) NA

Specifications

Tests



39

A.7: Bai-Perron Structural Change Test with Seasonal Adjustment and B = 1.

Note: see A.2 and A.3 A.8: Bai-Perron Structural Change Test with Seasonal Adjustment and B = 2.


zt = {1} q = 1 p = 2 h = 15 B = 1

SupFT(1) UDmax WDmax

17.577*** 17.577*** 17.577***

Sequential 1

LWZ 1

BIS 1

T1

1928:7**

(1928:5-1928:12)

Specifications

Tests



zt = {1} q = 1 p = 2 h = 15 B = 2

SupFT(1) SupFT(2) UDmax WDmax SupFT(2|1)

17.577*** 26.200*** 26.198*** 34.400*** 11.666**

Sequential 2

LWZ 2

BIS 2

T1 T2

1928:7** 1926:7**

(1928:6-1929:1) (1926:1-1926:8)

Specifications

Tests



40


Note: - At 2.5% level of significance, only T1 (1928:7) is chosen but at 1% level, no point is significant. - For others, see A.2 and A.3 A.10: Bai-Perron Structural Change Test with Seasonal Adjustment and B = 4.


zt = {1} q = 1 p = 2 h = 15 B = 3

SupFT(1) SupFT(2) SupFT(3) UDmax WDmax SupFT(2|1) SupFT(3|2)

17.577*** 26.200*** 11.112*** 26.198*** 34.399*** 11.666** 13.052**

Sequential 3

LWZ 2

BIS 2

T1 T2 T3

1928:7*** 1926:7** 1924:10**

(1928:6-1929:1) (1925:12-1926:8) (1924:3-1925:2)

Specifications

Tests



zt = {1} q = 1 p = 2 h = 15 B = 4

SupFT(1) SupFT(2) SupFT(3) SupFT(4) UDmax WDmax SupFT(2|1)

17.577*** 26.198*** 11.112*** 7.000*** 26.198*** 34.399*** 11.666**

SupFT(3|2) SupFT(4|3)

14.051** 8.600

Sequential 3

LWZ 2

BIS 2

T1 T2 T3

1928:7*** 1926:7** 1924:10**

(1928:6-1929:1) (1925:12-1926:8) (1924:3-1925:2)

Specifications

Tests



41



z t = {1} q = 1 p = 2 h = 15 B = 5

SupFT(1) SupFT(2) SupFT(3) SupFT(4) SupFT(5) UDmax WDmax

17.577*** 26.198*** 11.112*** 7.000*** 11.083*** 26.198*** 34.399***

SupFT(2|1) SupFT(3|2) SupFT(4|3) SupFT(5|4)

11.666** 14.052*** 8.600*** 0.000

Sequential 3

LWZ 2

BIS 2

T1 T2 T3

1928:7*** 1926:7** 1924:10**

(1928:6-1929:1) (1925:12-1926:8) (1924:3-1925:2)

Specifications

Tests



structural change in the job matching process before the great … · 1 structural change in the...

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