Minimum Wage and Export with Heterogeneous Firms

Transcription

1 Minimum Wage and Export with Heterogeneous Firms Churen Sun Shanghai Institute of Foreign Trade, Shanghai, Guoqiang Tian Texas A&M University, Coege Station, Tao Zhang Shanghai Institute of Foreign Trade, Shanghai, Abstract This paper proposes a two-country trade equiibrium mode with heterogeneous firms to investigate the infuence of minimum wage on firms exports. The theoretica anaysis postuates that the infuence of minimum wage on firms exporting probabiity and foreign saes is negative. Foowing econometric anaysis based on the firm-eve data (Annua Survey of Chinese Industria Firms) matched with prefecture-eve-city data incuding urban minimum wages from 1998 to 2007 verifies these predictions. Keywords: Minimum wage, heterogeneous firm, productivity, export JEL Subject cassification: F16 The research is funded by the Key Research Base of Humanities and Socia Science of Shanghai Municipa of Higher Education (Institute of Internationa Business, Shanghai Institute of Foreign Trade). Churen Sun gratefuy acknowedges financia support from Genera research for Humanities and Socia Sciences Project, Chinese Ministry of Education (Grant No. 09YJCZH074) and Innovation Program of Shanghai Municipa Education Commission (Grant No. 10YS168). Research Institute of Internationa Business, Shanghai Institute of Foreign Trade; Correspondence address: Rm. 701, Buiding 34, No.1099, Wenxiang Road, Songjiang District, Shanghai, China, ; Emai: sunchuren@gmai.com. Department of Economics, Texas A & M University, Coege Station, TX 77843, USA; Emai: gtian@tamu.edu. Correspondence address: Rm. 703, Buiding 33, No.1099, Wenxiang Road, Songjiang District, Shanghai, China, ; Emai: neotaoism@yahoo.com.cn.

2 2 SUN, TIAN AND ZHANG 1 Introduction China is a deveoping country and has achieved high economic growth, with annua GDP growth rates of around 10 percent over the past 30 years. Internationa trade hed an important roe in China s rapid economic growth and China has been considered to be the word factory up ti now under it s export-oriented poicy in the past three decades. This poicy succeeded ascribing to the ower wage paid to China tremendousy abundant abors. However, the centra government of China and oca governments of various provinces and cities 1 has increased the nomina monthy, daiy and houry minimum wage during the past twenty years. 2 With the disappearing of China s demographic dividend, more and more worries on China roe of word factory are paid to the increasing minimum wages. Continuing debates about positive and negative impacts of minimum wage on foreign trade emerges successivey in China. There are a arge number of advocates of the minimum wages, which argues that the increase of minimum wage wi ead to an increase in aggregate demand and economic growth. Under home market effect, this eads to the increase of the country s foreign export. Some argues that the increase of minimum wage wi have sma effects on production, business and empoyment. On the contrary, there are critics that the increase of minimum wage can resut in high production costs and unempoyment, and add burdens to enterprises, especiay when there is on-going economic stagnation and thus reduces their exports. However, the above arguments against or in favor of minimum wage on trade are often made without theoretica supports and empirica evidences. The question that how minimum wage affects internationa trade in China remains unanswered so far. The purpose of the paper is to investigate the infuence of the minimum wage on firms exports. This paper proposes a two-country and two-factor trade equiibrium mode with heterogeneous firms to investigate the impacts of minimum wages on firms exports. In our mode, firms are heterogeneous in productivity. A firm must pay a fixed entry cost before it observes its productivity, 1 Beijing first set a minimum wage in 1994, and many other provinces and cities set their minimum wages successivey. 2 A minimum wage is the owest monthy, daiy or houry wage that empoyers are compeed to pay to empoyees. It is expected to increase the iving standards of abors, especiay the poor and vunerabe. Moreover, it is generay considered to generate other effects such as promotion of aborers work and productivity, reduction of peope covered in subsidy programs, increasing consumption, aggregate demand and generation of mutipier effects, etc. In addition to these effects, it resuts in the increase of abor cost, which thus reduces firms output and abors hired.

3 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA 3 which is ex ante random. After that, it decides whether or not to start production. In the atter case another fixed production cost is incurred. Firms are heterogeneous both in terms of productivity. The firm empoys capitas and abors to produce its variety, where the price of capita is determined by the market whie that of abor is exogenousy determined and is usuay above its equiibrium eve. The firm can decide to export its product to the foreign market or not. In the former case it has to pay another exporting fixed cost. According to the above setting, we find that the increase of the domestic minimum wage decreases firms exporting possibiities by seection effect (i.e., forcing ow-productivity firms to exit the market) and decreases firms exporting saes by increasing their unit production costs. Moreover, firms productivity has positive impacts on their exports. In this paper, we appy firm-eve data from the Annua Survey of Industria Firms cross-sectiona data coected by the Nationa Bureau of Statistics of China from 1998 to 2007 to estimate the impacts of oca minimum wage on their exports. To reaize our theoretica postuation, we first estimate firm-eve productivity in each year and then regress firms exports with respect to their productivity, minimum wages, and other contro variabes. The empirica resuts verify our theoretic resuts. The rest of this paper is arranged as foows. Section 2 reviews the iteratures on the reationship between minimum wage and internationa trade. Section 3 introduces the cosed-economy mode with heterogeneous firms and minimum wages. Section 4 anayzes the open-economy mode and the impact of minimum wages on firms exports. Empirica modes, data treatments, summary descriptions of data incuding prefecture-eve-city monthy minimum wage, and productivity estimations are introduced in Section 5. Empirica resuts are stated in Section 6. Section 7 concudes the paper. 2 Literature review Literatures on the reationship between minimum wages and internationa trade can be cassified into two groups. One considers the case that inter-industry wages are distorted whie rea wages are fexibe. The other considers the case that a industria wages are distorted. Hagen (1958), Bhagwati and Ramaswami (1963) and Magee (1976) investigated the first case. Summarizing their findings, we can see that the increase of the minimum wage in an industry eads to the increase of capita intensity and the decrease of outputs within this industry and

4 4 SUN, TIAN AND ZHANG the decrease of capita intensities and the increase of outputs in other industries if capitas are industry-specific and abors are mobie across industries. This impies that the increase of the minimum wage in an industry eads to the increase of exports in this industry and the decrease of imports in abor-intense industries if the country exports capita-intense and import abor-intense goods before the change of minimum wages, vice versa. If abors are not mobie across industries, then the resuts sti hod as before. However, unempoyment occurs in the industry whose minimum wage increases. Haberer (1950), Brecher (1974a,b) investigated the second case. Brecher (1974a,b) anayzed the case with two countries, two goods, two factors and constant-returnto-scae production technoogies. They showed that the increase of the minimum wage in a abor-abundant country decreases the exports of abor-intensive goods and increases the exports of capita-intensive goods. The situation is reversed if the country is capita-abundant. The decrease of the minimum wage in a country may ead the reverse of trade directions. That is, the country may change to import capita-intensive whie export abor-intensive goods. Their modes were extended to the case with mutipe goods and mutipe factors by Schweinberger (1978), where the number of goods and that of factors are equa. Based on Schweinberger (1978) s idea, Brecher (1980) considered a sma-country open economy with three factors (capita, abor and and) and two goods. It found that the increase of the minimum wage in a country wi increase the exports of both capitaintensive and abor-intensive goods if the country speciaizes incompetey, the production technoogies of the two goods are constant return to scae and one good is more capita-intensive and more abor-intensive. Neary (1985) further investigated the case that the number of factors are arger than that of goods and concuded simiar resuts to those given in Brecher (1974a,b). The above findings may change if the interaction effects between endowment and trade structure are invoved into consideration. Fug and Gaor (1986) constructed a genera equiibrium with two countries, two goods and two factors (skied and unskied abors), where an unskied abor can change to skied abor by accumuating human capitas. It showed that the increase of the minimum wage on the unskied abors in a sma country eads to the increase of the exports of skied-abor-intensive goods if this country speciaizes incompetey. The resut is reversed if the country exports unskied-abor-intensive goods. The case for arge countries is a itte different. If the country exports unskied-aborintensive good at first, then the increase of the minimum wage on the unskied abors may reverse the trade structure. When the minimum wage is sufficienty

5 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA 5 high, the country wi speciaize in the production of and export the skied-aborintensive goods in the short run and its exports wi keep increasing in the ong run. The above researches are based on the assumption of homogeneous firms and their resuts are ony industry-eve. Firms heterogeneity needs to be considered to investigate the impacts of minimum wages on individua firms exporting behaviors. However, this can not be done under the frameworks of the Ricardian mode, the Heckscher-Ohin theory and the new trade theory. 3 In fact, few iteratures are focusing on this topic. This paper constructs a trade equiibrium mode with heterogeneous firms and minimum wages to investigate the impacts of minimum wages on firms exports. Different from Meitz (2003), countries in our mode are asymmetric and the number of factors is two (capita and abor). Because of the minimum wages on abor are above their market-equiibrium eves, ony the capita markets cears. Our mode is aso different from that in Egger et a. (2009), in which there is ony one production factor (abor) and there is one fina good and many intermediate goods whose number is endogenousy determined. Moreover, it did not investigate the impact of minimum wages on firms exports. According to our mode, we get the foowing main resut: the increase of domestic minimum wage wi decrease a firms exporting probabiities and their exporting saes. 3 Cosed economy with minimum wage and heterogeneous firms In the economy we investigate are there two countries (i.e., the domestic and the foreign country, denoted by H and F, respectivey). In each country, there are M monopoisticay competitive industries. We assume that each variety in each of which is produced by ony one firm. Suppose that there aren andn firms in industry inh andf, respectivey (hereafter we use * to index the corresponding variabes of F ). The production of each variety uses two factors, the capita (K) and the abor (L), where K is industry-specific, which is ony mobie within the 3 Many empirica resuts since 1990s have shown that firms in the same industry in a country have different exporting behaviors. First, exporters are reativey few among a firms in an industry. Second, exporters are reativey more arger and more productive. Third, most exporters exports ony a sma part of their outputs. Fourth, exporters performance variabes affect significanty and positivey their exports. Fifth, exporters have higher wages and higher innovation eves. Pease refer to Tybout (2003) for a survey of these iteratures and Meitz (2003) and Bernard et a. (2003) for theories deveoped to expain these phenomena.

6 6 SUN, TIAN AND ZHANG same industry, whie L is mobie across industries. As this paper does not investigate the impact of country size on firms exports, we assume that each country is normaized with one unit of infinitey divisibe abor. Suppose that the preferences of consumers of both countries are the same, which can be represented by the foowing utiity function U = M =1 ( N 0 ) β x ρ ρ i di, 0 < β,ρ < 1, M β = 1, (1) =1 whereβ represents the share of consumption in industry among tota consumption expenditure, ρ = σ 1 σ, σ is the substitution easticity between varieties in industry andx i is the consumption of varietyiin industry. Suppose that each consumer s income comes ony from his wage w. 4 As what is concerned in this paper is the impact of minimum wage standard on firms exports, we make the foowing assumption. Assumption 1 The minimum wages are higher than or equa to the market equiibrium wages in H and F, respectivey. Moreover, they are set so that each consumer in the two countries can get at east the minimum wage income. Our rationae to make Assumption 1 is of two fods: (1) If the minimum wage in a country is ower than the market wage, then it has no impact on the market equiibria, and thus we do not need to consider it. (2) If the minimum wage can not guarantee that a the abors s expected incomes are higher than it, then the minimum wage standard is of no sense. 5 Under Assumption 1, unempoyment occurs in the economy as the minimum wage is higher than the market equiibrium wage. Since firms are rationa, it s natura for them to pay abors with minimum wage if there s no incompete information or sticky abor market wage or other institutiona barriers. ( ) 1 N 1 σ Let the price index in industry bep, wherep = di, = 1,,M. p 1 σ 0 i Then the demand q i for and the expenditure r i on variety i in industry are, re- 4 When the firms entry attains its equiibrium, their expected profits are zero, so that each consumer s capita income is0. 5 The minimum wage standard which is higher than the market equiibrium wage aways eads to unempoyment, and thus each abor s income is equa to the unempoyment rate times the minimum wage. We do not investigate unempoyment by assuming that each abor gets the minimum wage at equiibrium foowing Mejean and Patureau (2010), whose economy consists of unskied and skied workers and the unskied ones get the minimum wage. Mejean and Patureau (2010) does this by assuming that there s an entirey ump-sum unempoyment benefits system, in which ump-sum taxes on empoyed workers are redistributed as ump-sum subsidies to those unempoyed ones. This assumption appies to this paper.

7 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA 7 spectivey, q i = Q ( pi P ) σ ( ) 1 σ pi, r i = R, = 1,,M, (2) where Q = β w P is the tota consumption andr = P Q = β w is the tota expenditure on varieties in industryin the economy. P Since a industries have simiar monopoistic competitive market structure, we ony consider the representative firm s behaviors in industry, and thus ignore the firm-indexiin the seque. Suppose the representative firm s production function is Y = θk α L 1 α (herein the capita-output easticity α varies with industries), where Y, K, L are, respectivey, the firm s output, capita and abor hired, and θ is it s productivity. In each industry, firms productivity is heterogeneous. Suppose that the distribution function of firms productivity in industry is of the foowing form: G (θ) = 1 (b /θ) k θ b, 0 ese, (3) whereb > 0 is the ower bound andk > 2 is the shape parameter ofg (θ), which measures the concentration degree of firms productivity distribution in industry. Each firm does not know its productivity eve before it enters into the market. It observes its productivityθafter it pays the industry-specific fixed entry costf, which is invested in the form of entrepreneur spirit but is measured by money. 6 After the representative firm observes its productivity, the firm needs to decide whether or not to produce and se its variety. In the former case, another fixed production costf is incurred, which is aso invested in the form of entrepreneur spirit but is measured by money. If the firm begins to produce and se its variety, it is faced with the demand function given in (2). Thus, its optima capita and abor inputs are, respectivey, K = ρ σ P σ Q 1 σ ( ) 1 θ σ r 1, L = ρ σ P σ α Q 1 σ ( ) 1 θ σ 1 w, (4) 1 α 6 Here we assume that entrepreneur spirits are suppied without easticity. It s worthy to point out that anaysis wi be much more compicated if the fixed entry cost F is invested in the form of abor or capita.

8 8 SUN, TIAN AND ZHANG ( ) α ( ) 1 α r where = w α 1 α is the unit production cost of varieties in industry. Therefore, the firms optima output and pricing rue are, respectivey, q = ρ σ P σ Q σ θ σ, p = ρ θ. (5) (5) impies that: (1) a firm s output is higher and its price is ower, the higher is its productivity; (2) a firm s output is ower and its price is higher, the higher is the industria unit production cost. The net profit of the firm with productivity θ in industry in each period is π = (1 ρ )D f, (6) where D = M θ σ 1 is the firm s domestic sae and M = ρ σ 1 P σ Q 1 σ. Define the weighted productivity eve as θ [ ] 1 + = θ σ 1 σ µ 0 (θ)dθ 1, where µ (θ) is the density function of productivity distribution of incumbents in industry. Then we have P = N 1 1 σ ρ θ, Q = N 1 1 σ β ρ w θ. (7) The firm decides to produce ony if π 0, from which we can get D and θ, the cut-offs of firms domestic saes and their productivity (such that the profit of the firms withd is zero): D = σ f, θ = ( ) 1 σ f β w σ 1 N 1 σ 1 θ. (8) This impies that the productivity cut-off θ is higher, the higher is the industria weighted productivity eve θ. According to the reationship between the ex post productivity distribution µ (θ) and the ex ante oneg (θ), and aso by the form ofg (θ), we rewrite the industria weighted productivity eve θ as θ (θ ) = ( k k +1 σ ) 1 σ 1 θ. (9) Substituting (9) into (8), we can sove the equiibrium number of firmsn as: N = β w σ f k +1 σ k. (10)

9 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA 9 This impies that the arger number of firms within the industry in equiibrium, the higher the minimum wage is. As the minimum wage is fixed above the market equiibrium wage, ony the capita market cears in equiibrium. Substituting (8), (9) and (10) into the cearing condition of capita market, we can sove the equiibrium interest of the capita in industry: r 1 = ρ β w K, (11) α which impies that the ower minimum wage and the higher capita stock ead to the higher interest of the capita in industry. This indicates that the increase of the minimum wage wi increase the industria unit production cost, which can be simpified as = (β ρ ) α (1 α ) (1 α ) K α w. Substituting (11) into (7), we can get the equiibrium expressions ofp andq, respectivey, as foows: P = N 1 1 σ β α ((1 α )ρ ) (1 α ) K α w θ 1,Q = N 1 1 σ (β ρ (1 α )) 1 α Kα θ. (12) Moreover, by (10), (12) and (6), we can find the equiibrium output of the firm with productivityθin industry as q = ρ k σ f θ σ k +1 σ θ1 σ 1, (13) which impies that the firm s output is higher, the higher is its productivity and the ower is the minimum wage. The free entry condition impies that each firm s ex ante expected net profit upon entry sha be zero, which determines the equiibrium number of incumbents in the industry. The entry condition can be written as foows: 1 G (θ ) f δ ( θ(θ ) θ ) σ 1 1 = F, (14) where δ is the surviva probabiity of firms in each period in industry. As G is given by (3), we can get the equiibrium productivity cut-offθ as foows: θ = ( f ) 1/k σ 1 b. (15) δ F k +1 σ

10 10 SUN, TIAN AND ZHANG According to (15) and the expression of θ(θ ), we know that both industria productivity cut-off and industria weighted productivity are not affected by the minimum wage eve. According to (9), (10), (15) and the fact σ > 1, (12) impies that industria price index P and industria output Q are higher, the higher is the minimum wage. One interesting resut is that industria output is positivey correated with the minimum wage, which impies that consumers tota consumption and hence their wefare increases with the increase of the minimum wage in the cosed economy under Assumption 1. 7 This resut has some seeming conficts with our initia intuition, as the increase of the minimum wage increases firms unit production costs. However, it hods because the increase of the minimum wage increases consumers demand and hence industria output. Summarizing above discussion, we have the foowing proposition. Proposition 1 In the cosed economy and under Assumption 1, the increase of the minimum wage wi increase industria capita interest, industria unit production cost, industria price index, industria output, and the equiibrium number of firms in the industry. Moreover, it wi decease each firm s output and increase their pricing rues. However, it does not change industria productivity cut-off and industria weighted productivity eve. We can expain the atter part of Proposition 1 as foows. Under Assumption 1, a abors get the minimum wage. Though the increase of the minimum wage increases firms unit production costs and thus the industria price index, it increases faster than the industria price index, and thus consumers purchasing powers increase, which attracts more firms to enter into the market. Furthermore, as a firms are facing with the same increasing unit production cost, the increase of the minimum wage does not change the industria productivity cutoffs and thus does not change the industria weighted productivity eves. Athough Proposition 1 hods in the cosed economy, it does not hod in the open economy. In the atter case, firms in the home country are facing with different increasing competition pressures from their foreign rivas - the competition power of domestic firms decreases whie that of foreign firms increases. Under 7 It seems that this resut wi cause the foowing paradox - the increase of the minimum wage wi increase consumers wefare infinitey. This paradox is caused by Assumption 1. As we argued that Assumption 1 hods conditionay, i.e., the tota output are arge enough to pay each consumer the minimum wage. However, this condition wi be broken when the minimum wage is set enough high.

11 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA 11 free trade, the increase of the domestic minimum wage wi increase industria productivity cut-offs and hence industria weighted productivity eves. 4 The impact of the minimum wage on the exports of heterogeneous firms 4.1 Equiibrium in the open economy Firms in industry must pay a fixed exporting cost κ to enter into the foreign market. Suppose the iceberg transportation cost is τ for transporting one unit of good from the home country to the foreign market. For simpicity, we assume that the corresponding variabesκ andτ in the foreign country are, respectivey, equa to those in the home country. Then the exporting profit of the firm with productivity θ in industry in the home country is: π X = max { 0,(1 ρ )M X θσ 1 κ }, (16) where MX = ρ σ 1 P σ Q 1 σ τ 1 σ, and P and Q are, respectivey, foreign industria price index and foreign tota output in industry. The firm chooses to export ony ifπ X 0, from which we can get the domestic and foreign exporting productivity cut-offs in industry, as foows: θ X = (N +N X ) 1 σ 1 θ X = (N +N X ) 1 σ 1 κ 1 σ 1 ρ τ [(1 ρ )β w ] κ 1 σ 1 ρ τ [(1 ρ )β w] 1 σ 1 1 σ 1 θ T, (17) where θ T and θ T are the domestic and foreign aggregate productivity, respectivey, which have the foowing forms: θ σ 1 T = k N θ σ 1 k +1 σ +N X θ σ 1 X N +N X, θ σ 1 T = θ T, k N θ σ 1 +N X θ σ 1 X,(18) k +1 σ N +N X in which N X and NX are, respectivey, the domestic and foreign numbers of exporters. After observing the exporting productivity cut-offs of domestic and foreign firms in industry, it s easy for us to find the productivity distributionsµ X (θ) andµ X (θ) of domestic and foreign exporters. When G (θ) adopts the form given

12 12 SUN, TIAN AND ZHANG in (3), we can concude the expressions of θ σ 1 T andθ σ 1 X, respectivey, as foows: θ σ 1 X Moreover, we have P σ = κ ( ) σ 1 ρ f Q = f τ σ 1 ( 1 ρ ρ ) σ 1 θ σ 1,θ σ 1 X = κ f and θ σ 1 T θ 1 σ, P σ Q = f τ σ 1 1 ρ from (18) and soveθ σ 1 X ( ) σ 1 ρ θ σ 1. (19) ( When a firm exports, its optima capita and abor inputs are K X = L X = [ ρ P Q 1 σ [ ρ P 1 Q σ τ 1 σ τ 1 σ θ ρ ρ θ ρ ρ ρ ) σ 1 θ 1 σ. (20) ] σ ( ) 1 r, (21) α ] σ ( ) 1 w. Under Assumption 1, ony the capita market cears. Hence according to the cearing condition of the capita market (20) and (21), we have α r α = r α = ρ k K 1 τ σ 1 [ ] f N +τ 1 σ κ N X, (22) (1 ρ )(k +1 σ ) ρ k K 1 (1 ρ )(k +1 σ ) τ σ 1 [ f N +τ 1 σ κ N X]. When G (θ) adopts the form given by (3), we can get an incumbent s ex ante exporting probabiity in industry as foows: ς = N X = 1 G ( ) [ k (θ X ) N 1 G (θ ) = θ κ = θ X f ( ) ] σ 1 k σ 1 ( ) k ρ θ θ. (23) Then the ex ante expected profit that a firm enters into the market is: π = π D ( θ )+ς π X ( θ X ), (24) where π D is the firm s expected profit from seing domesticay, and π X is its expected profit from seing in the foreign market. We thus have π = σ 1 (f +ς τ 1 σ κ ), π X = σ 1 τ 1 σ κ. (25) k +1 σ k +1 σ

13 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA 13 The sum of expenditures on industryfrom both countries is equa to that of a the firms profits in this industry in both countries. Therefore, we have f N +τ 1 σ κ N X +f N +τ 1 σ κ NX = k +1 σ β (w +w ). (26) σ 1 Moreover, suppose that the probabiity that a domestic firm in industry exits the market isδ. Then we have(1 G (θ )) π /δ = F for the ong-term entry condition, from which we have f N +τ 1 σ κ N X = k +1 σ N (σ 1)b k θ k. (27) (27) impies that a firm s ex ante exporting probabiity (equa to N X N ) is increasing in the productivity cut-off θ of entry into industry. Combining (27) with that of the foreign country, we can finay get Ω = ( θ θ ) k = ( f τ 1 σ κ ( f τ 1 σ κ κ f ρ σ 1 κ f ρ σ 1 ) k σ 1 ( ) k σ 1 ( ) k ) k. (28) (28) impies that Ω is decreasing in w if ω = / is increasing in w. This together with (23) yieds the foowing emma. Lemma 1 Under Assumption 1, ifω is increasing in the domestic minimum wage w, thenς is decreasing inw. That is, the increase of the minimum wage eads to the decrease of firms ex ante exporting probabiity. Proof. See the appendix. The economic intuition of Lemma 1 is rather straightforward. If the reative unit production cost of the home country to the foreign one increases with the domestic minimum wage in industry, then the reative variety price of the home country wi increase, and thus domestic firms competitive powers and their foreign sae profits wi decrease. This further makes ower-productivity domestic firms exit the exporting market. probabiity decreases with the domestic minimum wage. Therefore, domestic firms ex ante exporting From (23), we have N X = N ς, NX = N = ς. Substituting (19 ) into (20) and (18), we can get a two-equation system ofn andn. SubstitutingN X = N ς, N X = N = ς into the above system, we can find the expressions of N and N (see (37) and (38) in the appendix). Further, according to (26) and (27), we can

14 14 SUN, TIAN AND ZHANG finay get the foowing resuts: = β b k δ F E θ k w +w N +N Ω 1,θ k = β b k w+w δ F E N Ω +N. (29) Appying (37) and (38) in the appendix, we can prove the foowing emma. Lemma 2 θ is increasing inw. Proof. See the appendix. Lemma 2 indicates that the increase of the domestic minimum wage wi force the ow-productivity domestic firms to exit the market, which increase the average productivity of exporting incumbents in the home country. This further forces those ow-productivity firms in the foreign country to exit the market. And thus the exporting productivity cut-off in the foreign country increases. Finay, to find how the increase of the domestic minimum wage affects firms exporting behaviors in the home country, we need to know the reationship between have: and w. According to (22), (27) and the definitions of and, we = ( w ) ( ) α ( ) 1 α K N θ k α = w K N θ k ( w ) ( ) ( α ) α 1 α K N Ω w K N. (30) and w w and prove the fo- Using (30), we can anayze the reationship between owing resut. Lemma 3 Under Assumption 1, is increasing in the reative wage w. That is, w the increase of the gap between the domestic minimum wage and the foreign one wi increase the difference between the domestic and the foreign unit production cost for each industry. Proof. See the appendix. Lemma 3 indicates that the increase of the domestic minimum wage has different impacts on domestic and foreign industria unit production costs - the former increases more faster than the atter. This resut coincides with our intuition. 4.2 The impact of the minimum wage on firms exports According to the expression of M X, (20) impies that the increase of the domestic minimum wage wi increase industria exporting productivity cut-offs. More-

15 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA 15 over, by (20) and (16), if a firm exports, its exporting sae is X = f 1 ρ ) ( σ 1( θ θ ) σ 1. (31) From Lemma 3, is increasing inw, given the foreign minimum wagew. From Lemma 2,θ is increasing inw. Hence by (31) and Lemma 1, we have the foowing main proposition of this paper. Proposition 2 In the open economy and under Assumption 1, the increase of the domestic minimum wage wi decrease firms ex ante exporting probabiities and exporting saes. Moreover, firms exporting saes increase with their productivity eves. It s necessary to briefy iustrate Proposition 2. First, it impies that firms ex ante exporting possibiities and their exporting saes are a increasing with their productivity, which coincides with the theoretica resut proposed in Meitz (2003) and many other empirica iteratures. Second, as the main resut in the paper, the increase of the domestic minimum wage wi decrease firms ex ante exporting possibiities and their exporting saes. This resut is easy to understand. On the one hand, the increase of the domestic minimum wage may change the structure of comparative advantages between the two countries, so that the home country uses capitas whie the foreign country uses abors more intensey. This increases prices of capitas and thus those of firms exporting varieties. On the other hand, the increase of the domestic minimum wage wi increase the home country s demands for varieties of the foreign country and thus increases their prices. The synthetic effect is that the difference between the two countries industria unit production costs increases. Because of the same reason, the increase of the domestic wage wi seect ow-productivity domestic firms out of the exporting markets, and thus increase industria exporting productivity cut-offs in the home country. This further owers firms ex ante exporting probabiities. 5 Empirica modes According to (31), we know that minimum wage and firms productivity both affect firms exporting behaviors. In this section, we test their impacts on firms exports using firm-eve data from Annua Survey of Chinese Industria Firms. We first estimate firms productivity, and then regress firms exporting choices and

16 16 SUN, TIAN AND ZHANG exports with regard to minimum wage, their productivity and other contro variabes. 5.1 Firms exporting behaviors According to (31), we anayze the infuence of minimum wage on firms exporting behaviors by estimating the foowing equations: DX rit = τ r +η +γ i +λ t +ψnw rt +ζnˆθ rit +ϕz rit +ν ri +ǫ rit, (32) nx rit = τ r +η +γ i +λ t +ψnw rt +ζnˆθ rit +ϕz rit +ν ri +ǫ rit, (33) where DX rit is a dummy of firm i exporting state, with 1 for exporter and 0 for non-exporter, and X rit is firm i s exporting sae in period t, ˆθ rit is the estimated productivity of firm i in industry in region r in period t, λ t,η,γ i and τ r are, respectivey, time, industry, firm and region fixed effects, and Z rit is a vector containing firm i characteristics, incuding other prefecture-eve-city-eve and firm-eve contro variabes. The random effects, ν ri and ǫ rit, are normaydistributed i.i.d. random variabes with mean 0 and variances σ 2 ν and σ 2 ǫ, respectivey. Finay,r,,i,t are region, industry, firm and time indices, respectivey. 5.2 Data Source We match the city-eve macroeconomic data with ASIF to generate our empirica data. The city-eve data is coected from three major sources: China Urban Statistic Yearbook, China Statistic Yearbook and China Regiona Statistic Yearbook ( ). The firm-eve data is from the Annua Survey of Industria Firms (ASIF) that is coected by China Nationa Bureau of Statistics between 1998 and Here we mainy discusses the usage and treatments of ASIF dataset. This dataset contains a detaied information for a state-owned and non-state-owned firms above the designated scae 5 miion Yuan with a operationa, financia and manageria items in 40 2-digit industries and 90 4-digit and digit subindustries. The number of firms covered by this dataset is 165,118 in 1998 and 336,768 in 2007, respectivey. 8 8 The industry section of China Statistic Yearbook, China Industria Statistic Yearbook and reports in China Markets Yearbook are compied based on this dataset, which covers 95% of the industry gross output in these yearbooks (Lin et a. 2009; Lu and Tao 2009; Brandt et a. 2012). The ony difference between ASIF and China Industria Statistic Yearbook is that the ater is reported in aggregated industries and sectors whie the former is individua firms and pants.

17 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA Variabes Definition and Consistency Since 2003, the China Nationa Bureau of Statistics started to impement new Nationa Genera Specifications of Industry (GBT/4757), therefore there were two systems registered and coded in this dataset: before 2003 and afterwards. In this research, we adjust a industry-reated codes by the GBT/4757 system. Apart from these direct adjustments, we unify those variabes which are registered differenty in different years according to their expicit definitions. 9 By making the above adjustments, we are sure that the whoe dataset is consistent internay and tractabe in terms of both the cross-section and the ongitudina manner. 5.4 Missing variabes, missing vaues and treatments There are missing variabes and vaues in differenty years of ASIF. Missing vaues can be found in year 2001 to Some are due to statistica index changes or adjustments of accounting system. 10 Some are due to missing accounting. 11. Some of these variabes can be computed by accounting principes, 12 whie missing variabes ike tota export vaue (2004) can ony be cacuated by inear interpoation. We treat missing vaues with two principes: eaving a accounting variabes (operationa, financia and manageria variabes) unchanged, and 2) matching and refiing a possibe firm-idiosyncratic variabes, such as firm id, ocation and posta address, operation status, founding year, registration type, beonging, stock share, etc. This maximizes the coverage and usage of the ASIF dataset. First of a, we checked the dataset s firm id yeary. Not as simpe as previous research (Lin et a. 2009; Lu and Tao 2009; Brandt et a. 2012) that caimed that the ASIF dataset contains a unique firm id for each firm throughout the 10 years. Instead, there are repetitive firm ids in each year. 13 Comparing with the over- 9 For exampe, words ike gross vaue, net vaue, tota vaue, sum amount are missing in some case or years, fixed capita refers to the net vaue of fixed capita, asset refers to the gross vaue of asset, empoyment refers to the average empoyment numbers, etc. Since year 2004, the tota vaue of saes was no onger surveyed. Instead, this term was repaced by sum income of major revenue. And the geographic codes were argey extended to 12 digits since 2004 (6 digits for province-city-county, pus other 6 digits for viage-district-street accordingy). 10 For exampe, constant vaue of tota production vaue and product sae vaue are no onger accounted in the nationa survey between 2004 and For exampe, firm status (2001), firm size (2002, 2004), tota vaue of fixed capita (2003), tota export vaue (2004), current vaue of gross output (2004) and current vaue of saes (2005). 12 For exampe, the tota vaue-add equaizes sum of current vaue of output - midde inputs pus + vaue add tax. 13 There are totay 463 repetitive ids and one wrongy registered firm.

18 18 SUN, TIAN AND ZHANG a two miion firms dataset, those firms seems minute and no harm. However, many of them are arge SOEs, such as provincia petro ine companies, regiona tobacco companies and provincia eectricity groups who share the same registered names and are controed by the centra government. They are infuentia both in terms of oca gross domestic product, revenue, taxation income, industria forward-backward inkages as we as oca empoyment. Some of them are even 80 times arger than some ordinary firms. We beieve that deeting these repetitive firms coud cause the very probem of seection bias. To dea with this probem, we match these firms ocations, owners names (egaistic representative names), major product items, accordingy, and then assign these firms with new firm IDs in the ASIF dataset, respectivey. Secondy, we identify and recover missing vaues in variabes ike ocation, operation status, founding year, registration type, beonging and stock shares, respectivey. To save space, we ist here two exampes. Taking the operationa status in year 1999 as the first case. There are 3,904 firms that are either missing or noted as 0, capita A or etter a. We take these ots as the sub-database and match them with the sampes in 1998, 2000 to 2007, accordingy. Our rationae is that if these firms exited after year 1998, they woud not be accounted or noted in the 1999 survey, vice versa. If they appeared in the 2000 or ater years survey, their operationa status is active instead of frozen or cosed. In fact, there are 3,276 firms that were noted in the 1998 survey. Among the other 628 firms, 471 did not exist in the foowing years survey since We can thus safey concude that these 471 firms ony exist in year 1999 and their operationa status sha be registered as canceed (not beonged to status as estabishing, operating, frozen, or other ) by the end of this year. The second exampe is treating the missing vaues of ocation. Taking the ocation variabe in year 2000 as the case. There are 67 firms whose ocation codes are missing, noted as 0 or wrongy registered (some etters repaced the itera 6 digits ocation codes). Foowing the same way stated above, we match and sort these firms with pre- and after- years survey data. 57 firms among them were identified with survey data, 6 of the other 10 firms are found in the survey data. We match the eft 4 firms with their excusive information - phone number, mai address, firm name, major products and owner names, and finay find their ocation codes.

19 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA Further discussion of data treatment Some noteworthy drawbacks in the ASIF dataset need further discussions. We beieve that these probems are partia reasons causing arge estimation bias. The first is that the manufacturing firms covered in the samping periods increased dramaticay since the year Except that more and more firms annua saes reached the officiay designated scae, the year 2004 was an industry census year and there was more comprehensive survey coverage in it, which may expain the jump of the number of firms from 2003 to 2004 (Lu and Tao 2009). The second is ASIF does not cover sma non-state-owned firms with annua saes ess than five miion Yuan, which may resut in samping seection bias. The third is that ASIF does not provide information of organization reations among muti-pant firms. As we can not identify whether two firms beongs to the same enterprise, what we can do is ignoring the situation that enterprises have more than one pant. The disaggregate composition of firm TFP coud not refect some muti-pant firms rea performance. Comparing with researches appying the same data source, this research does not deete firms with zero monetary inputs or outputs (gross assets, net sum of fixed capita vaue, saes, gross outputs) or empoyments ess than 10 persons (Jefferson and Zhang 2008; Cai and Liu 2009). The endogeneity of firm behavior is our major concern. We are arguing that if researchers need to observe firms endogenous behavior, henceforth estimate their sef-adjustments in capitas and abor investments and yeary midde inputs from year to year, the zero monetary accounting is usefu and sensitive in indicating their entry and exit dynamics. Since we assume that firms are aware of their productivity changes as we as their profitabiity, there is ess soid ground to assume that they make static decisions responding to each year s productivity shock. Levinsohn and Petrin (2003) proposed a method (LP method) on firm-eve productivity estimation that ony requires information of midde input as the state variabe of capita stock. We appy the LP method to observe firms entry-exit dynamics in each year. To cross references, we aso appy the pooed OLS and the Fixed effect pane data method to estimate firms productivity. For the computation of tota factor productivity, gross production vaue, net saes of the pants, investment, midde inputs and a other monetary variabes were defated using price defators (1978 as the benchmark year).

20 20 SUN, TIAN AND ZHANG 5.6 Firm Productivity Estimation There are different methods to estimate firm-eve productivity, such as (semi-, non- ) parametric or stochastic frontier approaches, etc. In this chapter, we mainy appy the LP method to estimate firms TFP that was first proposed in Levinsohn and Petrin (2003) (see the appendix for detaied description of this method). The LP method has severa advantages over the other methods, such as the pooed OLS method, the fixed-effect method, etc (see Sun et a. (2011) for detaied comparisons about these methods as we as the OP method proposed in Oey and Pakes (1996)). 5.7 Minimum wage and urban amenities We aso coect data of minimum wages and other macroeconomic variabes of Chinese cities from 1998 to As there is not a uniformy statistica origin, we coect data of prefecture-eve-city monthy and houry minimum wages from websites and statistica buetins of oca governments. Though the Nationa Statistic Bureau does not report minimum wages, websites of most provinces, provincecapita cities governments provide their annua government working reports that contains oca minimum wages both in terms of monthy and houry scaes. But many periphera cities in Northwest China have poor pubic information service on their oca minimum wages or government annua reports. To sove this probem, we aso impement extensivey search of these cities oca Peope s Court Civi Judgments and Civi Affair Bureau s reports. For exampe, according to the Marriage Law of China, if the sponsor has no job or requires responsibe settements for divorce, the cacuation shoud be based on the oca monthy minimum wage. Moreover, socia compensation, pension and insurance payments are cacuated based on oca monthy minimum wages according to the Civi Affair Bureau s reguations. Hence, we can fi in these cities minimum wages by court judgements as we as some oca civi affair offices reports. Finay, we get totay 2850 minimum wages from 1998 to 2007, covering 85.33% of tota 334 prefecture-eve cities (autonomous prefectures or prefectures) a around China. Some schoars have two contrary doubts on minimum wage. The first is that minimum wage is not binding downward. That is, there are some abors whose rewards are ess than the minimum wage. We argue that even even if this case occurs, it s not sufficient to judge whether the atter is binding or not. This situation may happen as some forms of amenities and wefare provisions are suppied as the substitution to the monetary wage payment. For instance, some firms

21 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA 21 provide free shetering and food services in accounting to their ow wages, noncontract temporary workers in short period time with ow payments which are reported as firms average wage payments, and off-the-books income traditions in some firms who are giving bonus as the major incentive to motivate workers instead of given wages. Wang (2011) impemented an extensive nationwide survey on off-the-books income. It found a contradicting phenomenon that some househods consumptions are higher than their actua income reative to to payro received from work. The second is that the minimum wage is not binding upward. However, even if a firms pay their empoyers wages higher than the minimum wage, if does not iustrate that the minimum wage is binding for firm s wage decisions. In fact, if this case occurs, it impies that the hypothesis that the minimum wage is binding is not testabe as a firm s wage is not aways set at the minimum wage because of many factors, such as their monopoistic power, difference between its empoyees skis, abors wage expectation, empoyment search frictions, etc. For exampe, Berg (2003) shows that minimum wage wi push up market equiibrium wage because of the existence of search friction of the abor market and heterogeneity in the empoyees skis. Moreover, if abors are paid by their skis and the wage of the abors with the owest ski is binding at the minimum wage, then it s easy to deduct that other abors s wages are increasing in the minimum wage. This impies that the minimum wage is binding for a abors wages in this sense. We aso coect data of infrastructure of these prefecture-eve cities, incuding bus, road area, postoffice, tax, fisca expenditure and per capita city area. We measure human capita with average education year in a prefecture-eve city, which is cacuated by(primary 5+highschoo 12+coege 15), where primary, high schoo and coege are per capita primary, high schoo and coege students in the prefecture-eve city, respectivey. We measure provincia institution eve with the indices deveoped by Gang Fan and Xiaou Wang. 14 We match firm-eve data with prefecture-eve-city-eve data by firms ocation information and match those sampes with both firm-eve data and city minimum wages. We finay get totay 2,096,899 observation sampes within these years. However, we ony use data between 2004 and 2007 to do empirica anaysis to avoid possibe errors in this chapter according to the foowing rationaes. First, as queried by many researchers, the minimum wages were set too ow before 14 They pubished a sequence of books tited China Market Indices in China Economic science press from 1997 ti now, which measures provincia institution eves with 6 upper eve indices and many ower eve indices. See the books for detais. Here we ony use those from 1998 to 2007.

22 22 SUN, TIAN AND ZHANG 2004 and thus they may be ower than the market equiibrium wages. Second, 2004 is the year when the new cabinet appeared on the stage to start a new economic revoution, which infuenced thoroughy the deveopment trend of Chinese economy since then. Third, the statistica caiber of Chinese enterprises changed much after 2004 and thus many private enterprises were incuded into the survey. Tabe 1 in the appendix describes the minimum, maximum, mean, and median of minimum wages in each year in the whoe country. We can see that they are a increasing in time. It s easy to see that the mean firm wage in the whoe country in each year is aways arger than the maximum of the minimum wage. Moreover, the differences between minimum wages in different prefecture-eve cities are arge, which impies the arge deveopment and regiona differences between countries in China. Tabe 2 in the appendix shows the mean firm wage, minimum, maximum, mean, and median of minimum wages in each province in year We can see from both tabes that minimum wage is ess than the mean firm wage in each prefecture-eve city. According to our summary statistics on firm wages, we find that the minimum of them is arger than the minimum wage, which impies that the minimum wage is the ower bound of firm wage. [Tabe 1 is inserted here.] [Tabe 2 is inserted here.] 5.8 Summary statistics In our empirica anaysis, a region unit is a prefecture-eve city. A region s area A is the area of its metropoitan area. To contro some other factors that may affect firms exports, we invove firms ownership structure (state-owned, coectiveowned, private-owned, ect., here cassified by Stock dummy), beonging reationship (nationa, regiona, provincia, prefecture-eve-city-owned firms, cassified by Beonging dummy), size eves (cassified by Size dummy) and their operating status (cassified by Status dummy) for firm-eve characteristics (which is defined by China Statistica Bureau in the origina dataset), prefecture-eve-cityeve characteristics ike per capita human capita (denoted byhumancapita), tax (denoted by tax) and fisca expenditure (denoted by f iscaexpend), and institute index (denoted by institute) for province-eve one. Prefecture-eve city infrastructure is measured by per capita bus, road area and postoffice (denoted by

23 PRODUCTIVITY HETEROGENEITY, MINIMUM WAGE AND FIRMS EXPORTS IN CHINA 23 bus, roadarea, postof f ice, respectivey). We aso consider the infuence of industry and region that firms ocate on their exports, which is controed by industry - and region - dummy (cassified by Industry dummy and Region dummy, respectivey). In our baseine empirica anaysis, firms tota factor productivity is estimated appying the LP method, which is denote by ptfp. In the seque, we wi use productivity estimated using the OLS method (denoted byosbyind) to do robust anaysis. Tabe 3 shows the summary description of the main variabes interested in this chapter. We see in the tabe that the mean of city minimum wages from 2004 to 2007 is yuan, and there are 24.8% of exporters among the sampes. The average firm exporting sae is miion yuan and the average tota factor productivity in the sampe is The standard deviations of a the variabes impies that the difference between the firms is arge in many sides. [Tabe 3 is inserted here.] 6 Econometric resuts We regress Equation (32) in the first step appying the Probit mode to investigate how minimum wage affects firms exporting choices by controing other factors. In the second step, we examine the infuence of minimum wage on firms exporting saes using the Tobit mode (33). 6.1 The effect of minimum wage on firms exporting choices and saes This subsection reports the estimation resuts of the infuences of minimum wage on firms exporting choices (see Tabe 5) and saes (see Tabe 6), respectivey, which are estimated using (32) and (33) with Probit and Tobit modes. We see briefy from these two tabes that the infuence of minimum wage on firms exports are significanty negative in a estimation modes controing consecutivey firm-eve, city-eve, industry-eve and region-eve characteristics, such as firm tota productivity, city size, city fisca expenditure, city human capita and indices of urbanization economy, ocaization economy, diversification economy, competition economy and other firm specific effects. [Tabe 4 is inserted here.]