Silviase/jgov_v1.4_full_ann huggingface dataset:
Table 5: Result of Business Conditions Forecast : Real-time Data
Forecast	a > 50	a > 50	a ≤ 50	a ≤ 50	Accuracy rate (%)	FE	PT	New PT
Horizon (Months)	f > 50	f ≤ 50	f > 50	f ≤ 50
ft	19	1	4	8	84.4	32.18**	14.56**	13.42**
ft-1	22	2	4	10	84.2	24.06**	16.73**	15.01**
ft-2	21	1	5	9	83.3	32.88**	15.65**	14.25**
ft-3	22	1	6	8	81.1	26.08**	13.54**	12.14**
ft-4	21	2	7	7	75.7	9.72*	8.29**	7.27**
ft-5	20	2	11	3	63.9	2.65	1.12	0.55
ft-6	21	1	12	2	63.9	3.38	1.09	1.41
ft-7	20	2	13	1	58.3	0.77	0.04	0.51
ft-8	19	3	12	1	57.1	0.54	0.29	0.02
ft-9	20	2	13	0	57.1	0.00	1.29	0.69
ft-10	21	1	13	0	60.0	0.00	0.63	0.43
ft-11	19	3	12	0	55.9	0.00	1.85	0.86

Note: a, f, FE, PT and New PT denote actual data, forecast data, Fisher's exact test, Pesaran and Timmermann's (1992) test, and Pesaran and Timmermann's (2009) test, respectively.

$ ^{*} $ ( $ ^{*} $ ) indicates the rejection at 5% (1%) significance.

Table 6: Result of Business Conditions Forecast : Historical Data

Forecast	a > 50	a > 50	a ≤ 50	a ≤ 50	Accuracy rate (%)	FE	PT	New PT
Horizon (Months)	f > 50	f ≤ 50	f > 50	f ≤ 50
ft	19	2	4	7	81.3	14.69**	10.79**	9.27**
ft-1	22	3	4	9	81.6	14.84**	13.32**	9.88**
ft-2	21	2	5	8	80.6	15.09**	11.89**	9.85**
ft-3	22	2	6	7	78.4	11.74**	9.75**	8.37**
ft-4	21	3	7	6	73.0	5.67*	5.33*	4.41*
ft-5	21	2	10	3	66.7	3.04	1.48	0.96
ft-6	22	1	11	2	66.7	3.84	1.36	1.77
ft-7	21	2	12	1	61.1	0.88	0.01	0.65
ft-8	19	3	12	1	57.1	0.54	0.29	0.20
ft-9	20	2	13	0	57.1	0.00	1.29	0.69
ft-10	21	1	13	0	60.0	0.00	0.63	0.43
ft-11	19	3	12	0	55.9	0.00	1.85	0.86

Note: a, f, FE, PT and New PT denote actual data, forecast data, Fisher's exact test, Pesaran and Timmermann's (1992) test, and Pesaran and Timmermann's (2009) test, respectively.

$ ^{*} $ ( $ ^{*} $ ) indicates the rejection at 5% (1%) significance.
Table 7: Result of GDP Growth Forecast: Real-time Data
Forecast	$ a > 0 $	$ a > 0 $	$ a \leq 0 $	$ a \leq 0 $	Accuracy rate (%)	FE	PT	New PT
Horizon (Months)	$ f > 0 $	$ f \leq 0 $	$ f > 0 $	$ f \leq 0 $
$ f_{t} $	23	1	7	7	78.9	20.80**	11.48**	9.65**
$ f_{t-1} $	24	0	6	8	84.2	$ ^{a} $ inf**	17.84**	15.84**
$ f_{t-2} $	22	1	8	6	75.7	15.14**	8.65**	8.50**
$ f_{t-3} $	23	0	9	5	75.7	$ ^{a} $ inf**	9.76**	8.72**
$ f_{t-4} $	22	1	11	3	67.6	5.70	2.71	2.41
$ f_{t-5} $	21	2	12	1	61.1	0.88	0.01	0.01
$ f_{t-6} $	22	1	12	1	63.9	1.80	0.18	0.31
$ f_{t-7} $	21	2	12	0	58.3	0.00	1.23	0.96
$ f_{t-8} $	19	3	13	0	54.3	0.00	2.00	1.31
$ f_{t-9} $	21	1	13	0	60.0	0.00	0.63	0.32
$ f_{t-10} $	21	1	13	0	60.0	0.00	0.63	0.32
$ f_{t-11} $	22	0	12	0	64.7	0.00	$ ^{b} $ na	$ ^{b} $ na

Note: a, f, FE, PT and New PT denote actual data, forecast data, Fisher's exact test, Pesaran and Timmermann's (1992) test, and Pesaran and Timmermann's (2009) test, respectively. $ * $ ( $ ^{**} $ ) indicates the rejection at 5% (1%) significance.

$ ^{a} $ inf indicates infinity; when an FE test statistic is infinity, the hypergeometric distribution, which is identical to the FE test, is used to directly calculate the probability of significance.

$ ^{b} $ na indicates PT and New PT statistic couldn’t be calculated.

Table 8: Result of GDP growth Forecast : Historical data

Forecast	a > 0	a > 0	a ≤ 0	a ≤ 0	Accuracy rate (%)	FE	PT	New PT
Horizon (Months)	f > 0	f ≤ 0	f > 0	f ≤ 0
ft	24	1	6	7	81.6	24.93**	13.13**	11.51**
ft-1	24	1	6	7	81.6	24.93**	13.13**	11.70**
ft-2	22	2	8	5	73.0	6.47	5.13*	5.15*
ft-3	23	1	9	4	73.0	9.53*	5.25*	4.51*
ft-4	23	1	10	3	70.3	6.52	3.21	2.91
ft-5	22	2	11	1	63.9	1.00	0.00	0.00
ft-6	23	1	11	1	66.7	2.05	0.27	0.43
ft-7	22	2	12	0	61.1	0.00	1.09	0.85
ft-8	20	3	12	0	57.1	0.00	1.76	1.17
ft-9	22	1	12	0	62.9	0.00	0.55	0.30
ft-10	22	1	12	0	62.9	0.00	0.55	0.30
ft-11	23	0	11	0	67.6	0.00	bn	bn

Note: a, f, FE, PT and New PT denote actual data, forecast data, Fisher's exact test, Pesaran and Timmermann's (1992) test, and Pesaran and Timmermann's (2009) test, respectively. $ * $ ( $ ^{**} $ ) indicates the rejection at 5% (1%) significance.

$ ^{b} $ na indicates PT and New PT statistic couldn’t be calculated.
Table 9: Result of Leading Index
Forecast	a > 50	a > 50	a ≤ 50	a ≤ 50	Accuracy rate (%)	FE	PT	New PT
Horizon (Months)	f > 50	f ≤ 50	f > 50	f ≤ 50
$ f_{t-1} $	18	6	3	10	75.7	9.27**	9.52**	8.00**
$ f_{t-2} $	17	7	4	9	70.3	5.19*	5.67*	3.24
$ f_{t-3} $	17	7	5	8	67.6	3.73	3.77	2.43
$ f_{t-4} $	14	9	6	7	58.3	1.78	0.75	0.03
$ f_{t-5} $	15	8	5	8	63.9	2.90	2.48	1.23
$ f_{t-6} $	16	7	5	8	66.7	3.52	3.40	2.08
$ f_{t-7} $	14	8	5	8	62.9	2.72	2.15	1.78
$ f_{t-8} $	13	9	6	7	57.1	1.66	0.57	0.01
$ f_{t-9} $	15	7	5	8	65.7	3.30	3.03	2.69
$ f_{t-10} $	15	7	4	8	67.6	4.09	3.94*	2.27
$ f_{t-11} $	15	7	4	8	67.6	4.09	3.94*	1.95

Note: a, f, FE, PT and New PT denote actual data, forecast data, Fisher's exact test, Pesaran and Timmermann's (1992) test, and Pesaran and Timmermann's (2009) test, respectively.

$ ^{*} $ ( $ ^{*} $ ) indicates the rejection at 5% (1%) significance.

Table 10: Distribution of rates of Individual Forecasters' response

$ f_{t}^{j} $	$ f_{t-1}^{j} $	$ f_{t-2}^{j} $	$ f_{t-3}^{j} $	$ f_{t-4}^{j} $	$ f_{t-5}^{j} $
Expansion	mean	51.9	51.7	53.8	52.0	52.5	53.9
max	76.2	70.6	72.7	77.4	76.5	84.8
min	30.0	29.4	34.5	32.0	32.0	25.0
Contraction	mean	24.6	23.3	21.9	18.8	17.5	15.2
max	40.0	46.2	50.0	44.0	40.0	38.5
min	14.3	8.6	9.1	8.8	6.1	6.1
Flat	mean	23.5	25.0	24.4	29.2	30.0	30.9
max	44.8	57.1	48.5	55.9	55.2	55.6
min	3.8	5.7	7.7	8.8	8.8	9.1

$ f_{t-6}^{j} $	$ f_{t-7}^{j} $	$ f_{t-8}^{j} $	$ f_{t-9}^{j} $	$ f_{t-10}^{j} $	$ f_{t-11}^{j} $
Expansion	mean	56.0	57.9	60.3	62.9	64.8	65.4
max	84.8	87.9	87.5	90.0	93.3	90.3
min	39.4	39.3	42.3	41.9	43.8	44.4
Contraction	mean	12.7	12.5	12.7	9.7	8.3	9.4
max	33.3	41.7	44.0	39.1	34.8	33.3
min	3.0	3.0	3.1	0.0	0.0	0.0
Flat	mean	31.3	29.7	27.0	27.3	26.9	25.1
max	51.9	53.6	50.0	48.1	48.4	48.1
min	9.1	9.1	6.9	3.3	0.0	6.5
Table 11: Result of Business Conditions Forecast: All data Forecast Accuracy rate (%) PT

Forecast	Accuracy rate (%)	P1
Horizon (Months)	(Number of forecasters)
Mean	Max	Min	**	*
ft	74.5	93.8	45.0	8	4
ft-1	73.0	83.9	55.9	6	5
ft-2	72.2	87.9	56.3	3	3
ft-3	63.0	75.8	48.4	0	1
ft-4	60.0	75.8	41.9	0	0
ft-5	54.4	71.4	34.4	3	1
ft-6	50.9	69.7	33.3	0	9
ft-7	48.2	64.5	23.3	5	6
ft-8	49.6	65.5	29.0	5	5
ft-9	48.4	71.9	29.0	4	9
ft-10	48.3	68.8	25.8	5	9
ft-11	48.5	73.3	23.3	5	9

Note: All data includes Business Conditions forecast, Individual Forecasters, Real-time data. PT denotes Pesaran and Timmermann's (1992) test.

$ ^{*} $ ( $ ^{*} $ ) indicates the rejection at 5% (1%) significance.

Table 12: Result of Business Conditions Forecast: data excluding “Flat” answers

Forecast	Accuracy rate (%)	PT
Horizon (Months)	(Number of forecasters)
Mean	Max	Min	**	*
$ f_{t} $	86.4	100.0	64.3	28	3
$ f_{t-1} $	85.1	100.0	71.4	31	1
$ f_{t-2} $	82.3	100.0	67.9	23	7
$ f_{t-3} $	75.6	87.0	60.9	13	12
$ f_{t-4} $	69.7	86.4	47.6	2	9
$ f_{t-5} $	60.3	76.2	40.0	0	1
$ f_{t-6} $	56.8	73.1	35.7	0	0
$ f_{t-7} $	52.1	66.7	25.0	0	3
$ f_{t-8} $	53.7	68.4	34.8	0	3
$ f_{t-9} $	53.6	73.9	30.4	0	1
$ f_{t-10} $	52.9	73.9	29.4	0	1
$ f_{t-11} $	53.5	77.8	33.3	0	0

Note: All data includes Business Conditions forecast, Individual Forecasters, Real-time data. PT denotes Pesaran and Timmermann's (1992) test.

$ ^{*} $ ( $ ^{*} $ ) indicates the rejection at 5% (1%) significance.
New ESRI Working Paper Series No.16

The Dynamic Impacts of M&A on Target Firm's Labor in Japan

— Tentative Dynamic Panel Estimation by GMM —

Toshihiro Yamada and Hiroyuki Taguchi

May 2010

內閣府経済社会総合研究所

Economic and Social Research Institute

Cabinet Office

Tokyo, Japan
# The Dynamic Impacts of M&A on Target Firm’s Labor in Japan $ ^{*} $ — Tentative Dynamic Panel Estimation by GMM —

Toshihiro Yamada and Hiroyuki Taguchi $ ^{**} $

## Abstract

This paper provides a systematic empirical analysis of the effects of the M&A on target firm's employment in Japan. It may contribute to the Japanese literature by capturing the dynamic employment impacts of firm acquisition using latest micro data. Our main findings are: the immediate effects of firm acquisition on target firm's employment proved to be significantly negative presumably due to labor restructuring intended by the acquiring firm, while the negative effects do not appear to last as the subsequent dynamic impacts on target firm's employment.

Key words: M&A. firm acquisition, dynamic employment effects

JEL Classification Codes: D21, M51
### 1. Introduction

The merger and acquisition (M&A) in firms’ activities have shown the boom in recent years at the global level under the backgrounds of the progress of technological innovation and deregulation. Japan has been not an exception in the global boom, and experienced a rapid increase of the M&A activities since the later half of the 1990s. Although global credit shrinkage caused by US subprime loan turmoil and the subsequent deterioration of the real economy impacted the global M&A trends, Japanese M&A market still shows robust growth.

The impact of firm acquisition on the value of both the acquiring and the acquired firm has been the subject of a large and growing body of research literature. As for the effects on labor, there is a popular perception that the acquisition activity usually leads to, and indeed is often motivated by, the opportunity for substantial workforce reduction. This general interpretation was typically endorsed by an influential contribution of Shleifer and Summers (1988), which suggested that the control changes associated with acquisition activity offer an opportunity to firms to renege on implicit and explicit labor contracts, leading to a “breach of trust” with employees. On the other hand, acquisitions may occur because the firm believes it can manage the firm more efficiently than current management. The better management might lead to more and better jobs, particularly if new management has better access to capital markets for expanding the operation. While there exists an abundance of anecdote and general comment on the topic, there is very little systematic empirical evidence on the employment effects of firm acquisition and almost none in Japan. Furthermore, the limited existing literature – see Section 2 below – shows a variety of sampling procedures and methodologies and is also ambiguous in its findings.

This paper provides a systematic empirical analysis of the effects of the M&A on target firm’s employment in Japan. It may contribute to the Japanese literature by capturing the dynamic employment impacts of firm acquisition using latest micro data. The paper proceeds as follows. Section 2 describes the recent trend of the M&A in Japan, Section 3 summarizes the empirical literature and makes clear our position, Section 4 represents the empirical framework and estimation results, and the last section concludes.

### 2. Recent Trend of M&A in Japan

Japan has experienced so-called M&A boom since the later half of the 1990s. Figure
1 indicates remarkable increase in the number of M&A cases from around 500 cases in the mid of the 1990s to more than 2,000 cases in the 2000s, although showing its slight decline after 2007 due to the global credit shrinkage caused by the U.S. subprime loan turmoil (see Figure 1).

Looking at their composition by the types of M&A in Table 1, we can find the following characteristics. First, the number of M&A cases in which a Japanese firm acquired a foreign firm (“in-out” M&A) represents rapid growth in the later half of 1980s and rather stable trend thereafter. The share of “in-out” M&A also climbs to about 60 percent until 1990 and then continues to decline toward around 15 percent in 2008. The background of the “in-out” M&A boom in the 1980s is nothing more than the robust economy in that period, which had made Japanese companies go ahead into foreign markets, with the Sony Corporation’s acquisitions of CBS Records Inc. and Columbia Pictures Entertainment a typical example.

Second, the main element to create the 1990s-2000s M&A boom is the “in-in” M&A case, in which a Japanese company acquired another Japanese one. Its number as well as its share has grown up from around 200-300 cases (the share: around 50 percent) in the mid of the 1990s toward more than 2,000 cases (the share: about 80 percent) in the mid of the 2000s. The “in-in” M&A boom appears to come mostly from the necessity of industry consolidation amid intensifying international competition. In the steel industry, for example, two of Japan’s major steelmakers – Kawasaki Steel Corp. and NKK Corp. – were merged into JFE Holdings, inc. in 2002 in response to the fierce competition with their South Korean and Chinese counterparts. The individual companies’ efforts to reorganize group companies with the introduction of new accounting rules on a group-wide basis, may contribute to the “in-in” M&A boom.

Lastly, another element for the 1990s-2000s M&A boom is the “out-in” M&A case, in which a Japanese company was acquired by a foreign one. The number increased from around 50-60 cases in the mid of the 1990s toward about 200 cases in the mid of the 2000s. The “out-in” M&A can often be seen as a case for strengthening the domestic presence of foreign companies, with the City Group’s acquisition of the Nikkou Cordial group in 2007 a typical example. The activated role of foreign investment funds seems to have contributed to the increasing “out-in” M&A.

For investigating the factors behind the 1990s-2000s M&A boom, Arikawa and Miyajima (2007) picked up two different hypotheses and examined which hypothesis is applicable to Japanese M&A boom. The first hypothesis, which is often referred to as a neoclassical explanation, focuses on industry-level shocks to growth opportunities and profitability as a factor of M&A. Mitchell and Mulherin (1996) and Harford (2005),
recognizing that M&A activities concentrate in specific industries, argued that the occurrence of shocks to growth opportunities and/or profitability that require a large-scale intra- or inter-industry redistribution of resources leads to a boost in the number of M&A as an efficient means of reallocating resources. The other hypothesis is called “market-driven,” based on the assumption of stock market mispricing. Shleifer and Vishny (2003) theoretically showed that managers of bidding companies, when they have the information that the market valuation of their companies is higher than their fundamental value, have an incentive to seek profits by making acquisitions in stock-for-stock deals; and that myopic managers of target companies have an incentive to sell their companies, in disregard of the long-term profit prospects, by agreeing to favorable terms offered by bidders.

Arikawa and Miyajima (2007) examined the hypotheses above by using industry-by-industry data as well as individual companies' data. Their findings supported not the “market-driven” hypothesis but the neoclassical explanation; the 1990s-2000s M&A boom in Japan comes from some sort of shock that impacted the growth opportunities and profitability of the industry. $ ^{1} $ Miyajima et al. (2007) also stated that the recent, rapid increase in M&A in Japan has been driven by economic shocks - both positive and negative - such as technological innovation and sharp falls in demand, and that the increasing M&A have facilitated resource allocation in terms of downsizing less profitable divisions and expanding high-growth divisions, thereby contributing to the improvement of organizational efficiency through the transfer of management resources and know-how. Those findings that the M&A in Japan has been driven by real shock tempt us to recognize the significance in examining the labor impact of the M&A in later section.

### 3. Previous Studies and Our Position

Evidence on the overall employment impact of the M&A has been very limited. In addition, the limited evidence has been based on a variety of sampling procedures and methodologies, and has reported mixed findings. We first pick up several representative studies in the United States of America (USA), European countries including the United Kingdom (UK), and Japan.

As for the literature in the USA, Brown and Medoff (1988) examined the effects of
firm’s control changes with a large sample of firms in the state of Michigan. Their results suggested that the employment consequences depend upon the type of control change; Asset disposals were followed by a decrease in employment, while true mergers produced a small increase. The generality of the results is open to question, because their data set is numerically dominated by very small firms and excludes interstate acquisitions, where large-scale takeovers predominate. McGuckin et al. (1995), in a study using US plant-level data, reported that employment in acquired plants increased relative to that in non-acquiring firms, but suggested this was accompanied by improved operating efficiency, particularly in the smaller plants in their sample. However, when the authors used firm-level data they found no significant employment consequences. In a more recent study, McGuckin and Nguyen (2001) argued that ownership changes are not a primary vehicle for cuts in employment and wages, or closing plants, and instead, ownership changes are associated with increases in employment for the entire US manufacturing sector.

Concerning the literature in European countries, Conyon et al. (2002) provided a systematic empirical analysis of the effects of take-over and merger activity on firm employment in the UK using a specially constructed database. They indicated that significant rationalizations in the use of labor occur as firms reduce joint output and increase efficiency post-merger, and that these effects are particularly pronounced in the case of related and especially hostile mergers. On the other hand, Amess and Wright (2007), using a unique hand-collected dataset, examined the effects of leveraged buyouts on wages and employment in the UK. They found that all leveraged buyouts taken together have an insignificant effect on employment growth but have significantly lower wage growth than non-leveraged buyouts. Lehto and Böckerman (2008) examined the employment effects of M&A by using establishment-level data from Finland, and found that the cross-border M&A lead to downsizing in manufacturing employment as well as the changes in ownership associated with domestic M&A also causing employment losses.

As long as we see the previous works above, the evidence of labor losses by M&A appears more often in European countries than in the USA. Here comes Gugler and Yurtoglu (2004), which compared the effect of merger and acquisition on employment in Europe and the USA. While they did not find adverse effects of mergers on labor demand in the USA, they did find negative effects in Europe of the order of minus 10% compared to pre-merger levels. They attributed this significant difference to more rigid labor markets in Europe than in the USA.

Evidence on the employment impact of merger and acquisition has been extremely
limited in Japanese literature. To our knowledge, the only systematic empirical study is found in Kubo and Saito (2007). They focused their analyses on the merger’s impact on employment, and examined the 114 cases of mergers during the period from 1990 to 2003 among companies whose stock is listed on the Tokyo Stock Exchange. They found that during the post-1999 period the mergers brought about the effect on employees’ reduction by ten percent on average, and that the effect varied depending on the purpose of mergers as well as pre-merger firm’s performance; the mergers within the related industry, and the ones intended for firm relief produced more curtailment of employees than the average.

This paper tries to extend the fore-mentioned research literature, mainly of Kubo and Saito (2007), in the following directions. First, we focus our analysis on the employment impacts of the firm acquisition, whereas Kubo and Saito (2007) concentrate only on the merger’s effects on employment. In fact, the cumulative number of the acquisition case is more than that of the merger case during the 2000s. Second, we capture the dynamic employment effects of firm acquisition through using latest micro data, while the earlier study estimated only the immediate employment effects.

### 4. Empirical Studies

We now turn to empirical studies of the effects of firm acquisitions on acquired firms' employment in Japan. Before stepping into the analyses, we first clarify the used data and methodology, and then exhibit the estimation results and their interpretations.

### 4.1 Methodology

An ordinary dynamic labor demand function, assuming that output constrained firms face continuous quadratic adjustment costs and use a Cobb–Douglas technology, takes the following form of equation (see Bresson et al. (1996) or Nickell (1984) for a full exposition):

$$ l_{\mathrm{it}}=\alpha l_{\mathrm{it-1}}+\beta_{1}q_{\mathrm{it}}+\beta_{2}q_{\mathrm{it-1}}+\gamma_{1}(w/c)_{\mathrm{it}}+\gamma_{2}(w/c)_{\mathrm{it-1}}+\delta_{\mathrm{t}}D_{\mathrm{t}}+f_{\mathrm{i}}+\varepsilon_{\mathrm{it}} $$

where $ l_{it} $ , $ q_{it} $ and $ (w/c)_{it} $ denote the logarithms of employment, real output and real wages relative to user cost of capital of firm i in period t. $ D_{t} $ are a set of time dummies to account for technical progress and business cycle effects, and $ f_{i} $ are firm-specific fixed effects, which subtract firm-specific means from all the variables removing all time
invariant determinants of labor demand growth. $ \varepsilon_{it} $ is an equation disturbance term.

Our method of estimating the impact of M&A on employment is by the introduction of dummy variables. Since the sufficient data for output, wages and user cost of capital are not available as explained later, the variables of real output and relative input prices are omitted from our estimation. Thus, the estimated equation is composed of employment, the dummy related with M&A, time dummies and firm-specific dummies. It has to be notified that in the following estimations we focus only on the employment effects of not acquirer but target firm.

For the purpose of capturing the dynamic employment effects of M&A, we specify the estimated equations in the following two ways. The first one is to simply slide the M&A dummy. To put it concretely, we estimate the following equations step by step.

$$ \begin{aligned}l_{it}&=\alpha_{0}l_{it-1}+\lambda_{0a}DA_{it}+\lambda_{0b}DI_{it}+\lambda_{0c}DE_{it}+\lambda_{0d}DM_{it}+\delta_{t}D_{t}+f_{i}+\varepsilon_{it}\\l_{it}&=\alpha_{0}l_{it-1}+\lambda_{0a}DA_{it}+\lambda_{0b}DI_{it}+\lambda_{0c}DE_{it}+\lambda_{0d}DM_{it}\\&\quad+\lambda_{1a}DA_{it-1}+\lambda_{1b}DI_{it-1}+\lambda_{1c}DE_{it-1}+\lambda_{1d}DM_{it-1}+\delta_{t}D_{t}+f_{i}+\varepsilon_{it}\\l_{it}&=\alpha_{0}l_{it-1}+\lambda_{0a}DA_{it}+\lambda_{0b}DI_{it}+\lambda_{0c}DE_{it}+\lambda_{0d}DM_{it}\\&\quad+\lambda_{1a}DA_{it-1}+\lambda_{1b}DI_{it-1}+\lambda_{1c}DE_{it-1}+\lambda_{1d}DM_{it-1}\\&\quad+\lambda_{2a}DA_{it-2}+\lambda_{2b}DI_{it-2}+\lambda_{2c}DE_{it-2}+\lambda_{2d}DM_{it-2}+\delta_{t}D_{t}+f_{i}+\varepsilon_{it}\end{aligned} $$

where DA, DI, DE and DM are the M&A dummy: “firm acquisition”, “capital participation”, “capital increase”, and “merge” respectively. $ ^{2} $ For instance, if the firm i is acquired by another firm in the period of t, $ DA_{i} = 1 $ after the period of t continuously. The key statistics of interest, $ \lambda_{0} $ , measure the immediate impact of M&A on labor demand in percentage terms relative to the non-M&A labor trends, and $ \lambda_{1} $ , $ \lambda_{2} $ , $ \cdots $ represent the dynamic impact on the post-M&A employment.

Another way for capturing the dynamic employment effects of M&A is to insert the post-M&A trend dummy into the equation. Specifically, we estimate the following equation.

$$ \begin{aligned}l_{\mathrm{it}}=\alpha l_{\mathrm{it-1}}&+\lambda_{\mathrm{a}}DA_{\mathrm{it}}+\lambda_{\mathrm{b}}DI_{\mathrm{it}}+\lambda_{\mathrm{c}}DE_{\mathrm{it}}+\lambda_{\mathrm{d}}DM_{\mathrm{it}}\\&+\lambda^{\prime}{}_{\mathrm{a}}TDA_{\mathrm{it}}+\lambda^{\prime}{}_{\mathrm{b}}TDI_{\mathrm{it}}+\lambda^{\prime}{}_{\mathrm{c}}TDE_{\mathrm{it}}+\lambda^{\prime}{}_{\mathrm{d}}TDM_{\mathrm{it}}+\delta_{\mathrm{t}}D_{\mathrm{t}}+f_{\mathrm{i}}+\varepsilon_{\mathrm{it}}\end{aligned} $$