Sunk Costs of Exporting and the Role of Experience
in International Trade
Philipp Meinen∗†
April 2012
Abstract
This paper estimates the importance of destination-specific sunk costs of exporting. Particular focus is put on investigating the extent to which they can be reduced by firms’
previous experiences in interactional trade. The importance of sunk costs is inferred from
the state dependence of firms’ export activities in a market. Unlike other studies, additionally to unobserved heterogeneity, the error term is allowed to follow an AR1 process. This
turns out to be important for estimating true state dependence; neglecting the AR1 error
process amounts to substantially underestimating country-specific sunk costs. Moreover, I
find that previous experience in international trade reduces the role of market-specific sunk
costs by 36%. Export experience from other markets is particularly important for explaining this result suggesting that sunk costs of exporting can be distinguished into general and
market-specific costs. If the firm has previous export experience from a country with similar
characteristics (e.g. language) like the new one, export market entry is further facilitated.
Finally, the results show that importing from a market can induce starting to export there.
This suggests that market-specific knowledge from importing eases export market entry.
Results from jointly estimating firms’ export and import participation equations show that
the effect also exits for the opposite direction.
—
Keywords: Transaction-level Trade Data, Sunk Costs, Maximum Simulated Likelihood
JEL-Codes: F10 L10 D21
∗
[email protected]; Department of Economics and Business, Aarhus University
†
I am grateful to Christian Bjørnskov, Shigeki Kano, Jan de Loecker, Alfonso Miranda, Eduardo
Morales, Steve Redding, Alejandro Riano, Frederic Warzynski, and to the participants at the 2011 annual
meeting of the European Economic Association, at the 2011 Danish International Economics Workshop,
and at the 2011 annual GEP post graduate conference. I acknowledge financial support from The Tuborg
Foundation.
1
1
Introduction
Since the seminal work by Roberts and Tybout (1997) many empirical studies have illustrated the importance of sunk costs of exporting by depicting the strong state dependence
of firms’ export decisions.1 A common feature of these studies is that they base their analyses on the firm level while sunk costs of exporting may very well vary at the country
level.2 The present study extends Roberts and Tybout’s approach to the firm-country
level and pays special attention to the role that experience plays for sunk costs. Experience
may matter for sunk costs in different ways. First of all, if sunk costs of exporting can be
distinguished into general and market-specific costs, a firm that exported to some market
in the previous year does not need to consider the general costs again when deciding to
enter a new market this year. Furthermore, if the market to which the firm exported in
the previous year is similar in some characteristics (e.g. geography or culture) to the new
market, this may further ease entry into this market (Morales et al., 2011). Finally, if the
firm imported from the new market in the previous year, this may provide the firm with
relevant knowledge about the country facilitating the export market entry.
This study therefore relates to a recent literature on export market entry into individual markets with special focus on experience. Albornoz et al. (forthcoming) emphasize
the role of export experience by modeling firms’ export decisions as sequential. They
suggest that firms are uncertain about their ability as exporters and learn about it only
if they start exporting. Hence, firms first enter one market, learn about their exporting
profitability and then increase exports sales in the first destination and start exporting
to other markets or withdraw from exporting, respectively. They present evidence supporting the model’s predictions using Argentinean data. Morales et al. (2011) suggest
that a firm’s export decisions with respect to different countries are interdependent in
1
Bernard and Wagner (2001) for Germany, Bugamelli and Infante (2003) for Italy, Bernard and Jensen
(2004) for the US, Campa (2004) and Manez et al. (2008) for Spain, Das et al. (2007) for Columbia,
Requena-Silvente (2005) for UK SMEs, and Muuls and Pisu (2009) for Belgium
2
More recently, there are studies with similar identification strategies that consider the firm-country
level in their analysis. Gullstrand (2011) analyzes the Swedish food sector, Medin and Maurseth (2012)
analyze the Norwegian seafood exports, and Moxnes (2010) analyzes the non-oil manufacturing sector in
Norway. These studies also find significant state dependence of exporting activities in individual markets.
2
that exporting costs to a specific market may be lower if the firm already exports to a
country which has similar characteristics. The idea is that experience from markets with
certain cultural or geographical characteristics eases entry into markets with similar attributes. They present evidence for this mechanism using Chilean data. A similar idea is
put forward by ? using Chinese data and Lawless (2011) using Irish data. Moxnes (2010)
motivates an empirical model where he distinguishes between global and country-specific
sunk costs. He estimates the model on Norwegian data concluding that sunk costs are
largely destination-specific while the analysis is restricted to five destination markets.3
The present paper incorporates the ideas of general gains from export experience as
well as specific gains from experience depending on the characteristics of markets already
served. Additionally, in the model motivated below, market-specific knowledge from import activities may ease starting to export to a country. This mechanism is different from
other studies about the interdependence of exporting and importing. Those studies are
usually conducted at the firm level and assume that importing leads to exporting through
a productivity channel; i.e. importing leads to productivity improvements helping firms
to bear the sunk costs of exporting (Kasahara and Lapham, 2008; Bas, 2010). The empirical model in this paper is very flexible in that it does not impose any assumptions on
the direction of causality; instead both mechanisms are allowed for, i.e. importing may
induce exporting and vice versa.
In section 2, I motivate a discrete choice model of firm export participation in a country
with market-specific sunk costs which can be perceived as less important depending on
the firms’ export and import history in this and other markets. The identification of the
sunk cost parameter requires the estimation of true state dependence which is why I allow
for a complex error structure with unobserved heterogeneity and an autoregressive process
of order one (AR1). While the former assumption on the error structure is standard, the
latter is new for models of firms’ export participation in individual markets. A reason
for neglecting an AR1 error process may be that Roberts and Tybout (1997) did not
3
Further note that Lawless (2009) presents descriptive evidence for the importance of general sunk
costs of exporting using Irish data. Eaton et al. (2007) present similar evidence using Columbian data.
Moreover, Medin and Maurseth (2012) present evidence for sunk costs specific to countries and products
using Norwegian data.
3
find a significant AR1 process in their study. However, their results are obtained from
estimations with the firm-year pair as observational unit which is different from the firmcountry-year triad as analyzed in this study. It is possible that shocks to a firm are purely
transitory, while shocks to the firm-country combination are serially correlated. In fact,
if a firm’s strategy is that of an optimal export portfolio where firms engage in different
markets and diversify risks across markets, shocks to the firm-country combination would
even be expected to be correlated while shocks to the firm would be purely transitory.
That is why I allow for an AR1 error process in this study and obtain an estimate for
the degree of persistency of the transitory error component. The model is estimated by
maximum simulated likelihood (MSL) as well as a two-step approach based on GMM and
minimum distance techniques. In an extension of the model, I allow the unobservables
which affect firms’ export and import decisions in a country to be correlated by jointly
estimating the export and import participation equations. This approach allows for crossequation state dependence without imposing any assumptions on the direction of causality
between export and import decisions. As a side effect, this approach sheds some light
on determinants of firms’ import decisions and sunk costs of importing. This may be of
interest when considering recent studies which point out that firms’ import behavior is
very similar to their export behavior (e.g. Bernard et al., 2007) and which suggest that
importing is also characterized by sunk costs (e.g. Vogel and Wagner, 2010).4
The analysis is based on register data containing balance-sheet information and transactionlevel trade data for firms from the furniture manufacturing sector in Denmark which is
described in section 3. This is an interesting sector to study for the current purpose due
to its high involvement in international trade. The firms in this sector are very successful globally and source an important share of their inputs from abroad. Moreover, many
firms are two-way traders enabling an investigation of the relationship of firms’ export and
import activities in different markets. Estimations are performed on a balanced panel as
well as an unbalanced panel to assess the sensitivity of the results to a potential selection
bias.
4
Sunk costs of importing are e.g. related to search costs for potential suppliers, the inspection of
products, the contract negotiations and the learning and acquisition of customs procedures.
4
The estimation results presented in section 4 show that allowing for a complex error
structure is important for identifying true state dependence. The transitory error component is estimated to be significantly negatively correlated. This result is obtained from the
MSL and GMM / minimum distance estimators and from estimations on the balanced
and unbalanced panels. Neglecting an AR1 process in the error therefore amounts to
substantially underestimating the role of destination-specific sunk costs. Allowing for an
AR1 error process also turns out to be important for the predictive power of the model
which improves sharply when the AR1 process is introduced.
The MSL estimates from the preferred non-linear model suggest that destinationspecific sunk costs are important; a firm that has exported to a market last year is 47%
more likely to export to this market today compared to a firm with no export and import
activities in the previous year. The role of these costs can, however, be downsized by
experience from exporting activities in other markets and/or import experience. Results
from the MSL estimations show that controlling for general export experience and import
experience reduces the role of destination-specific sunk costs by 36%. The effect of general
export experience from other markets is very important for explaining this finding suggesting that global costs of exporting are relevant. The results further indicate that gains
from exporting to other markets are particularly high if the firm has experience from a
market with cultural or geographic characteristics similar to the new country. This is in
line with the mechanism described by Morales et al. (2011). The role of experience of
importing from a market for firms’ exporting decisions with respect to this market is also
estimated to be economically and statistically significant.
Results from the joint estimation of firms’ export and import participation equations
suggest that the effect from lagged importing on current exporting is of similar magnitude
as the effect from lagged exporting on current importing. This implies that importing
from a market can indeed facilitate starting to export there and vice versa. As sunk costs
are usually thought of being related to information gathering costs5 , an explanation for
5
Common examples of sunk costs of exporting are information requirements about business practices,
customers’ tastes, competition, and distributors in the foreign markets. Sunk costs of importing are e.g.
related to search costs for potential suppliers, the inspection of products, the contract negotiations and
the learning and acquisition of customs procedures (e.g. Vogel and Wagner, 2010).
5
this finding is that conducting one activity in a market provides the firm with relevant
market-specific knowledge which facilitates beginning also the other activity there.
2
Econometric Approach
2.1
A Simple Model
Roberts and Tybout (1997) develop a multi-period model of firms’ export participation
with sunk costs of exporting. I extend this model to the destination level where firms face
country-specific sunk costs of exporting. In this simple setup, entry into specific markets
may be easier (i) if firms have knowledge about a market from exporting activities in
this country two or more years ago, (ii) if firms have market-specific knowledge due to
importing activities in this country, and/or (iii) if firms have exporting experience from
other markets. This latter point may be particularly relevant if firms have experience
from markets which are similar to the new destination market in some characteristics
(Morales et al., 2011)
ex
In the model, firm i exports in period t to market d (yidt
= 1) if expected profits
associated with exporting to market d in year t are positive. Gross profits πidt depend
on firm characteristics and exogenous macro-level variables and need to be adjusted for
sunk (entry) costs of exporting Fid0 . If the firm has exported to market d in year t − 1,
it does not have to pay Fid0 in period t. Further, if the firm has last exported to d in
year t − j (j ≥ 2), the firm faces entry costs of Fidj < Fid0 . This assumption implies
that a firm can preserve market-specific knowledge from exporting activities two or more
years ago which may facilitate re-entering the market in period t. Moreover, the firm may
im
benefit from importing activities in market d in period t − 1 (yid,t−1
= 1). This is because
importing from market d may provide the firm with relevant knowledge about market d
easing export market entry in year t by Tid . Also exporting to other markets than country
ex
d (−d ) in the previous year (yi−d,t−1
= 1) may ease entry into d in year t by Gi . Reasons
for this latter assumption may be that firms do not have to repay general sunk costs
of exporting in this period or that knowledge from exporting to other, possibly similar,
6
markets facilitates entry into market d in year t. Finally, leaving the export market d
implies exit costs of Lid . Period t exporting profits from market d are then given by
ex
ex
im
ex
Ridt = yidt
[πidt − Fid0 (1 − yid,t−1
) + Tid yid,t−1
+ Gi yi−d,t−1
−
Jid
X
ex
ex
ex
] − Lid yid,t−1
(1 − yidt
)
(Fidj − Fid0 )ỹid,t−j
j=2
ex
with ỹid,t−j
=
Qj−1
k=1 (1
ex
− yi,t−k
) taking the value 1 if the firm last exported to market d j
years ago and 0 otherwise. Solving a simple dynamic programming problem leads to the
following dynamic binary choice equation:
ex
yidt

∗
ex
im
ex


1 if πidt
− Fid0 + (Fid0 + Lid )yid,t−1
+ Tid yid,t−1
+ Gi yi−d,t−1


P it
ex
=
(Fid0 − Fidj )ỹid,t−j
+ Jj=2
≥0



 0 otherwise,
(1)
∗
with πidt
denoting the increment to gross future profits for firm i from exporting to market
d in period t.6 Equation (1) implies that the importance of country-specific sunk costs
of exporting, the relevance of general export experience and the importance of import
experience from a specific market can be inferred from dummy variables indicating firm
i’s export and import participation in markets d and −d.
2.2
Econometric Model
Equation (1) readily leads to an estimation equation by specifying a reduced form empir∗
ical model approximating πidt
− Fid0 by
∗
πidt
− Fid0 = x0idt β + µt + εidt ,
(2)
where xidt refers to a set of control variables that vary at the firm and destination levels, µt
are time fixed effects and εidt is an error term. To be precise, I control for the productivity
6 ∗
πidt
= πidt + δ[Et {Vid,t+1 (Ωi,t+1 )|yidt = 1} − Et {Vid,t+1 (Ωi,t+1 )|yidt = 0}; see Roberts and Tybout
(1997) for details.
7
(TFP7 ), size (number of employees) and the 4-digit NACE industry classification of the
firms.8 Existing studies show that size and productivity are important determinants
of firms’ export participation possibly because they allow firms to overcome the sunk
costs of exporting (e.g. Bernard and Jensen, 2004). Both variables are lagged by one
year to alleviate endogeneity concerns. At the country level I control for market size
(GDP), population, changes in the bilateral exchange rate and bilateral distance between
Denmark and the foreign market. All independent variables (except for changes in the
bilateral exchange rate which can be negative) are log transformed. I then assume that
sunk costs do not vary across firms and define γ1 = Fd0 + Ld , γj = Fd0 − Fdj (j = 2, . . . , J),
γm = Td , and γg = Gd and substitute (2) into (1) to obtain the following binary choice
model
ex
yidt

 1 if x0 β + γ 1 y ex + PJ γ j ỹ ex + γ m y im + γ g y ex
id,t−j
id,t−1
i−d,t−1 + µt + εidt ≥ 0
idt
id,t−1
j=2
=
 0 otherwise .
(3)
The error term εidt consists of a time-constant component αid and a transitory component
ωidt . This distinction is important in order to estimate true state dependence. If ignored,
the serial correlation induced in εidt by αid would be picked up by the lagged dependent
variable and therefore misinterpreted as an indication of sunk costs. Note that αid allows
for persistent differences in firms’ profits from exporting to specific markets, e.g. caused by
general differences in managerial abilities or specific knowledge of managers about certain
markets. αid is assumed to be i.i.d. normal across firms and countries with variance σα2
and COV(xidt , αid ) = 0.
Another source of spurious state dependence is serial correlation in the transitory error
component. I account for this by assuming ωidt = δωid,t−1 + νidt where νidt is i.i.d. normal
across firms, countries and time. If shocks are persistent (high δ), sunk costs of exporting
may be less relevant as firm-country combinations with a positive shock today believe
7
TFP is estimated structurally following Wooldridge (2009). See the appendix for details on the
estimation approach.
8
The furniture manufacturing sector (NACE 3-digit sector 361) can be subdivided into five 4-digit
NACE sectors.
8
that this situation will persist in the future leading to high entry. This persistency of
the transitory shock would be picked up by γ1 if ignored and therefore falsely attributed
to high entry costs (Bernard and Jensen, 2004). On the other hand, a negative δ would
imply an underestimation of sunk costs. The assumptions made on the error structure
imply that the correlation of εidt over time depends on two components; namely λ =
2
σα
2 +σ 2
σα
ω
and δ. Note that for estimation purposes σω2 is normalized to unity. Roberts and Tybout
(1997) allowed for a similar error structure in their study and did not find any significant
effect from δ.9 As mentioned in the introduction, shocks related to firms’ export activities
in individual countries may be more plausibly believed to be serially correlated rather
than shocks affecting the whole firm. For instance, shocks to the terms of trade with one
specific market may be considered to be persistent while shocks to the whole firm (e.g.
related to business cycle movements) are more likely to be perceived as transitory.
2.3
Identification
The importance of sunk costs and experience is inferred from dummy variables indicating
firms’ export and import participation in markets d and −d. The identification strategy
for sunk costs is similar to that in Roberts and Tybout (1997). According to equation (1),
∗
a firm persistently exports to market d either if sunk costs are high or πidt
is high. Hence,
∗
identification comes from comparing the participation decisions of firms with similar πidt
ex
ex
im im
ex
ex
ex
, yi−d,t−1
) is
, yid,t−1 ), and (yi−dt
. Variation in (yidt
, yid,t−1
), (yidt
and differences in yid,t−1
therefore crucial for identification. Moreover, as Moxnes (2010) points out, identification
ex
of the parameter on general export experience additionally depends on variation in yidt
between destinations within firms; i.e. firms’ export participation in different markets
has to vary. Similarly, identification of the import experience parameter in the export
equation requires that firms’ import activities vary between destinations and in particular
ex
im
that (yidt
, yidt
) are not perfectly collinear.
9
Note that the studies cited in footnote 1 which use Roberts and Tybout’s model to estimate the
importance of sunk costs for different countries do not allow for an AR1 process in the error. The main
reasons for this are the insignificance of δ in Roberts and Tybout’s study and that allowing for δ makes
the estimation computationally expensive.
9
It is helpful to keep in mind that the intuition for identification of the general export
experience parameter is that exporting to some market facilitates exporting to another
market and the intuition for the identification of the import experience parameter is that
market-specific knowledge from importing can induce export activities in that market.
2.4
2.4.1
Estimation
Nonlinear Models
Initial conditions
The binary nature of the dependent variable suggests maximum likelihood (ML) as a
natural estimation choice. One aspect that needs to be addressed here is the initial
condition problem to prevent an upward bias of the sunk costs parameter (Stewart, 2007).
The problem arises because the history of the stochastic process under investigation is not
observed from its beginning and it is unlikely that the initial conditions are exogenous to
αid . The most commonly applied solution to this problem goes back to Heckman (1981)
who suggests to approximate the conditional distribution of the initial conditions by a
reduced-form expression using pre-sample information. In the present setup, firms’ export
behavior is observed in years 1 . . . T and the lag structure reaches back for J years. Hence,
equation (3) can be estimated for the years J + 1 to T and information from the years
t ≤ J is available to use Heckman’s approximation to solve the initial condition problem:
ex
yidt

 1 if x0p β p + µ + εp ≥ 0
t
idt
idt
=
 0 otherwise ∀ t ≤ J,
(4)
where the superscript p indicates pre-sample information.10 I assume a similar error structure as before for εp and allow the random effects in the pre-sample and sample periods to
p
p
+ νidt
).11 The system of equations (3) and (4) is then
be correlated (εpidt = ηαid + δ p ωid,t−1
10 p
x contains the same explanatory variables as before. Additionally, I supplement xp by firm-level
variables lagged by two years and destination market GDP lagged by one year.
11
Note that I follow Stewart (2007) and restrict η to be positive.
10
estimated jointly. This solution to the initial condition problem has been used widely and
shown to perform well (e.g. Akay, 2009). Moreover, this solution allows to deal with the
AR1 structure in a natural way.
Approximating the integral
The AR1 error structure introduces another estimation issue by requiring the evaluation
of a T-dimensional integral of normal densities which renders standard ML infeasible. I
therefore resort to maximum simulated likelihood (MSL). In particular, I use the GHK
algorithm of Geweke, Hajivassiliou and Keane as described in Lee (1997) to estimate the
model. I drop the id subscripts in the following presentation and only consider a one-year
lag structure to ease notation. Lee suggests to generate u1 , . . . , uT −1 independent uniform
[0,1] random variables and to obtain α from a N(0,1) random variable generator. The
random variables ν1 , . . . , νT −1 can then be generated recursively from t = 1 to T − 1 by
computing
ex
+ σα α + δωt−1 ))] and
1. νt = −kt Φ−1 [ut Φ(kt (x0t β + γ 1 yt−1
2. updating the error process ωt = δωt−1 + νt ,
where kt = (2yt − 1) and Φ (Φ−1 ) is the (inverse) normal cumulative distribution function.
Collecting the RHS variables except for the error components of the main and pre-sample
equations into zt and ztp respectively, the simulated log likelihood for each firm-country
pair with R generated random variables is given by12
L=
N
R hY
J
T
n1 X
io
X
Y
(r)
(r)
ln
Φ kt (ztp + ησα α(r) + δωt−1 ) ×
Φ kt (zt + σα α(r) + δωt−1 )
R r=1 t=1
1
t=J+1
The only requirement for consistency of this estimation routine is that R tends to infinity
as the number of observations N tends to infinity; in particular, R should increase at a
√
rate larger than N to ensure asymptotical accordance to standard ML (Lee, 1995, 1997).
I generate the random variables from Halton sequences instead of pseudo-random draws
12
See also Greene (2003) for an illustration of the MSL approach for a random effects probit model.
11
as they have shown to provide better accuracy with fewer draws. For instance, for the
case of mixed logit models, better accuracy is achieved with 100 Halton draws than with
1000 pseudo random draws (Train, 2009). The number of draws is an important issue in
order to obtain consistent results, while there is no clear guidance on what is the right
number. Lee’s (1997) Monte Carlo experiments for dynamic discrete choice models suggest no significant increase in estimation accuracy from above 50 pseudo-random draws.
The following MSL estimations are based on 100 Halton draws13 and maximization is
done using a Quasi-Newton method (DFP - Davidon, Fletcher, and Powell).
Joint estimation of export and import decisions
A final estimation issue relates to the lagged import variable in the export equation. If
unobserved heterogeneity of a firm’s export decisions is correlated with that of its import
decisions, joint estimation of firm’s export and import participation is required in order
to distinguish cross-equation state dependence and correlated unobserved heterogeneity
(Stewart, 2007). This implies that I have to specify an import participation equation.
Recent studies point out that firms’ import behavior is very similar to their export behavior (e.g. Bernard et al., 2007) and that importing is also characterized by sunk costs
(e.g. Vogel and Wagner, 2010). I follow this literature and model firms’ import decisions
similar to their export decisions by also considering sunk costs and the role of experience.
I then estimate both participation equations jointly using a bivariate dynamic discrete
choice model. I drop the AR1 error structure for this purpose as otherwise estimations
become computationally infeasible. I assume that the time-constant error components
in both equations (αex , αim ) are jointly normal with variances σα2 ex , σα2 im and correlation
ρα and that the transitory error components (ωex,t , ωim,t ) are jointly normal with unit
variances and correlation ρω .
The initial condition problem is again addressed by Heckman’s approach. I follow
13
In the appendix, I compare results obtained from estimations with 100 and 250 draws. The coefficient
estimates are very similar; this is particularly true for the coefficient of interest on lagged export status.
Moreover, the appendix contains estimation results on simulated data which allows to compare actual to
estimated parameters.
12
Alessie et al. (2004) and include the individual-specific effects αex and αim in both presample equations and allow them to be freely correlated between equations. To ease
notation, define kth = (2yth − 1) with h = (ex, im). Collecting the parameters to be
estimated into θ, the likelihood function becomes
Z
J
Y
Z
l(θ) =
αex
Φ2 ktex (z ex,p + η1 αex + η2 αim ), ktim (z im,p + η3 αim + η4 αex ), ρp∗
)
ω
αim t=1
×
T
Y
Φ2 ktex (ztex
+
αex ), ktim (ztim
+
αim ), ρ∗ω
φ2 αex , αim dαex dαim ,
t=J+1
where Φ2 denotes the bivariate standard normal cumulative distribution function and
φ2 (·) is the bivariate normal distribution of aex and aim with variances (σa2ex , σa2im ) and
correlation ρa .14 Estimation of this model requires the evaluation of a double integral
for which no analytical solution is available. I address this issue by again resorting
to MSL using an estimation algorithm similar to that in Kano (2008) and Miranda
(2011). I generate Halton sequences and calculate the corresponding values following
a standard normal distribution using the inverse-probability transformation. Next, I
generate R bivariate normal random variables per firm-country pair by Cholesky factor(1)
(1)
(R)
(R)
ization [(aex , aim ), . . . , (aex , aim )] and approximate the individual likelihood by l(θ) =
QT
QJ
PR
PR
1
Φ
Φ
·
×
·
.
(r)
(r)
2
2
t=1
t=J+1
R
α :r=1
α :r=1
ex
im
Average partial effects
To evaluate the economic meaning of the coefficient estimates of the non-linear models,
I calculate average partial effects (APE). Following Wooldridge (2005), I obtain APEs
from
N
−1
N
X
i=1
Φ(x0idt β̂a
+
ex
γ̂a1 yid,t−1
+
J
X
ex
ex
im
+ γ̂ag yi−d,t−1
+ µ̂ta ),
+ γ̂am yid,t−1
γ̂aj ỹid,t−j
j=2
14
Note that technically the model is identified by functional form. Nevertheless, Miranda (2011) suggests to add exclusion restrictions to help identification. I follow his strategy here. First, similar to
the univariate model, I add additional lags of the firm-level variables and destination market GDP to
the pre-sample equations. Second, the variable general export experience is excluded from the import
equation and general import experience is excluded from the export equation.
13
where the subscript a indicates multiplication by (1 + σ̂a2 )(−1/2) . This approach implies averaging out the unobserved time-constant error component. I calculate counterfactual outcome probabilities at the sample mean by fixing the coefficients of interest
(γ 1 , γ 2 , γ 3 , γ m , γ g ) at zero and then changing them to unity one by one.
2.4.2
Linear Probability Model
To assess robustness of the estimation results, I also estimate equation 3 in a linear
probability framework. The advantage of a linear probability model is that it allows to
treat the unobserved heterogeneity α as fixed so that the assumption COV(xt , α) = 0 is
not required. Moreover, by using a GMM approach for estimation, endogeneity concerns of
export and import variables can be addressed in a common IV setting. The big drawback,
however, is that point estimates are less reliable.
A common approach to estimate a model like equation (3) in a GMM setting is to
take first differences to eliminate α and then to instrument for the endogenous lagged
ex
using lagged values of ytex for years t ≥ 2 (Arellano and Bond,
dependent variable ∆yt−1
1991). Blundell and Bond (1998) propose a more efficient estimation approach by also
making use of information from the untransformed equation. In this case, additional
moments can be used by differencing the instruments to make them exogenous to the fixed
effects; i.e. instead of using lagged levels as instruments for the current first differences of
the dependent variable, they suggest to instrument current levels by lagged differences.
Blundel and Bond construct a system estimator which allows them to exploit the new
moment restrictions while keeping those from the difference GMM estimator. They do so
by building a stacked data set with twice the observations; the original transformed (first
differenced) variables and the untransformed variables. This system is then treated as a
single equation and estimated by GMM. This approach therefore uses additional moment
restrictions which can be checked by overidentification tests.15
This kind of estimator runs into problems if ωt follows an AR1 process as allowed for
15
See Roodman (2009) for more details on these estimation routines and their implementation in Stata.
14
in the non-linear model. Hyslop (1999) offers a solution to this problem which also allows
to obtain an estimate for the AR1 parameter δ. He points out that partially differencing
the levels equation eliminates the serial correlation in the error:
ex
− δγ 1 yt−2 + x0t β − x0t−1 δβ + (1 − δ)α + νidt
ytex = (δ + γ 1 )yt−1
(5)
ex
ex
This equation can then be consistently estimated using ∆yt−1
and ∆yt−2
to instrument
ex
ex
for yt−1
and yt−2
. Similarly, the estimation equation in differences can be estimated by
ex
− δγ 1 ∆yt−2 + ∆x0t β − ∆x0t−1 δβ + νidt
∆ytex = (δ + γ 1 )∆yt−1
(6)
ex
where yt−2
is a valid instrument for ∆ytex . Hyslop proposes a two-step approach to obtain
the structural parameters (β, γ, δ); first estimate equation (5) or (6) to get the reducedform parameter estimates and then use minimum distance techniques in a second step to
obtain (β, γ, δ). I follow a similar strategy here while I use the system-GMM estimator
of Blundell and Bond (1998) in the first step to increase efficiency. The standard errors
in the second step are obtained by bootstrapping around the whole procedure using 400
replications. Note that this two-step approach does not allow to estimate the parameters
on export experience from a market two or more years ago. Instead, I will estimate the
ex
ex
in the
and (∆)yt−4
effect of a three-year lagged dependent variable by including (∆)yt−3
estimation equations.16
3
Data
3.1
Data Sources
The analysis in the present study is based on firms with at least 10 employees from the
furniture industry (3-digit NACE rev.1.1 code 361) in Denmark. The sample reaches from
1996 to 2006 containing 759 of such firms. The sample therefore contains 11 years while
16
See the appendix for details on the minimum distance estimator.
15
it is worth noting that the first two years of the sample cannot be used for estimations
due to lagging firm-level variables by one year and using additional lags of the firm-level
variables as exclusion restrictions in the pre-sample equation of the non-linear estimation
approach. The estimation sample therefore reaches from 1998 to 2006. The AR1 error
structure in the econometric analysis requires a balanced sample to estimate the nonlinear model. While a balanced panel circumvents problems related to modeling firm
creation and destruction, it introduces a potential sample selection bias. To address the
sensitivity of the results, I also perform estimations on an unbalanced panel. Due to the
lag structure in the empirical analysis, a minimum requirement also for the unbalanced
panel is that firms remain in the sample for at least four consecutive years. After imposing
this condition and cleaning the data17 , 106 and 340 firms are left for the analysis on the
balanced and unbalanced panels, respectively.
The data mainly consists of register data from Statistics Denmark. I merge firmlevel balance-sheet information to the foreign trade statistic from Danish customs using
a unique firm identifier. The trade data is available on the transaction level providing
information on exports and imports to destination and from origin markets, respectively.
Given the large computational burden of MSL, I constrain the number of countries considered in the analysis to 55.18 These countries account for 95% of total exports and
imports of the firms in the unbalanced sample. I finally merge foreign market information
to the data set; GDP (constant USD 2000) and population data is sourced from World
Development Indicators19 , bilateral distance data is taken from CEPII, and exchange rate
data is obtained from Penn World Tables.
3.2
The Furniture Industry in Global Markets
The furniture industry in Denmark is very successful on the global market. The high
quality of the products and the focus on design are important features of this sector. The
17
Firms with negative domestic sales, firms that leave the sample and reappear later, and firms which
switch sectors during the sample period are dropped.
18
In total, the firms in the sample trade with 153 countries.
19
Note that GDP data for Taiwan is taken from Penn World Tables.
16
sector is also characterized by a high import activity sourcing from abroad an important
amount of inputs used in production. This combination of strong export orientation
and reliance on imported materials makes the sector an interesting case to study the
relationship between exporting and importing.
Tables 1 to 3 present some statistics about this sector based on the unbalanced sample.
Table 1 row (i) shows that the number of firms decreases over the sample period which
is in line with the general trend in the manufacturing sector in Denmark (Andersen
et al., 2012). Next, rows (ii) and (iii) indicate the strong involvement of these firms in
international trade by presenting export to sales and import to materials20 ratios. Between
one quarter and one third of the industry’s output is sold abroad and between one fifth
and one quarter of the materials are imported. Finally, rows (iv) and (v) present the
average number of export destinations and origins of imports. On average firms in this
sector export to 6 to 7 markets and import from 3 to 5 markets suggesting that firms’
importing activities are more concentrated with respect to foreign markets.
The furniture manufacturing sector can be further divided into five 4-digit NACE subcategories. Table 2 presents total export-to-sales ratios by 4-digit sector over the sample
period. It can be seen that most firms belong to the sub-sector ”other furniture” which
sells almost 40% of its output abroad. Moreover, Table 2 lists the ten most important
2-digit HS product categories for imports. Besides raw materials like wood and metal,
firms import more sophisticated inputs such as plastics, paper, and glass. Table 3 shows
to which countries the exports are mainly shipped and from where the imports mainly
originate. In both cases the EU15 countries dominate the top 10 countries in terms of
total values of shipments.
3.3
Descriptive Evidence
Table 4 presents summary statistics for the balanced and unbalanced samples, respectively,
for the data used in estimations; i.e. 1998 to 2006. The table groups the firms by their
20
Materials are obtained by subtracting value added from turn over.
17
trading activities; i.e. no trader, only importer, only exporter and two-way trader. The
observational unit in the econometric analysis is the firm-country-year triad; in total
52,470 observations are available for the balanced panel and 109,670 for the unbalanced
panel. In both cases the clear majority of observations relates to non-traders (i.e. firms
that do not trade with a specific country in a given year) followed by only exporters while
only importers form the smallest group. The unconditional means of these groups suggest
a ranking in terms of productivity and size going from non-traders in the bottom over
only importers and only exporters to two-way traders in the top.
Note that many firms indeed engage in exporting and importing with the same country in a given year. This observation may be suggestive for a relationship between firms’
exporting and importing activities in a country. As mentioned in the introduction, studies
analyzing the relationship between exporting and importing usually suggest that importing leads to exporting via a productivity channel (Kasahara and Lapham, 2008; Bas,
2010). However, according to the data presented here, firms rather first export to a market and then start importing from this country. The numbers in Table 4 may therefore
suggest a relationship between the two activities based on market-specific knowledge. The
relationship between exporting and importing will be further analyzed below where the
dynamics of exporting and importing are allowed to be interrelated without making a
priori assumptions on the direction of causality.
Next, I present some descriptive evidence on the role of general export experience with
the help of a transition matrix out of and into exporting.21 The upper part of Table 5
depicts changes in the number of export markets served in period t for firms grouped by
the number of destination markets served last year. The matrix shows that dynamics are
increasing in the number of destinations served in t − 1. In particular, if a firm has not
exported in t − 1, it is very likely that the firm still does not export in period t. However,
once a firm has exported in t − 1, the probability of changing the number of destination
markets increases rapidly with the number of markets served in t − 1. This clearly points
towards the importance of general export experience. I will further investigate this issue
21
See Lawless (2009) and Eaton et al. (2007) for export transition matrices for Ireland and Columbia.
18
in the next section where the importance of experience is also allowed to differ according
to the characteristics of markets served.
Remember that I analyze the relationship between exporting and importing by jointly
estimating the export and import participation equations where import participation is
modeled equivalent to export participation. To give some further motivation for this
approach, I present a similar transition matrix for import activities in the lower part of
Table 5. The picture drawn by this matrix is very similar to that from the exporting
matrix. Both panels show that experience indeed seems to play an important role for
firms’ export and import participation in individual markets. Together with the evidence
from existing studies, this suggests that a similar modeling approach for export and import
participation is adequate.
The picture drawn by the export transition matrix suggests that firm export activities
in individual markets are indeed fairly dynamic once a firm exported to at least one
market in the previous year. This finding may in fact be interpreted as an indication of
low-destination specific sunk costs. Eaton et al. (2007) present a similar transition matrix
for Columbian firms and supplement this evidence with information about the number
and trade volume of single-year exporters. They show that single-year exporters are an
important phenomenon in the data and therefore responsible for a considerable part of
the dynamics depicted by the transition matrix. Moreover, they show that these firms
only export on small scales. Their interpretation of this finding is that by exporting only
a small amount, these firms can circumvent paying sunk costs and test the market for
some time. If the test was successful, firms increase their sales to the market and thereby
lock into it; otherwise they withdraw from the market.22 To check whether a similar
interpretation is warranted in the Danish example, I present similar evidence as Eaton
et al. (2007) in Table 6 by depicting the number and trade volume of export starters,
stoppers, continuing exporters and single-year exporters. Export starters are defined as
firms that do not export to market d in t − 1, but export to d in t and t + 1. Export
stoppers export to market d in t − 1 and t, and do not export there in t + 1. Single-year
22
See Akhmetova (2010) for a model incorporating that idea.
19
exporters export to d in t while not exporting there in t−1 and t+1. Finally, continuously
exporting firms export to market d in all three periods. I present averages over the sample
period in Table 6 where single year exporters are also a considerable number, while their
export sales are low. This is in line with the hypothesis of Eaton et al. (2007). Moreover,
the numbers suggest that export starters and, in particular, continuously exporting firms
have much larger exporting sales in individual markets which could be an indication of
destination-specific sunk and fixed costs of exporting which require higher sales to be
covered.
The presence of single-year exporting firms in the data may have several implications
for the consecutive analysis. On the one hand, they may simply imply low state dependence of exporting activities in individual markets. On the other hand, it may be that
these firms experience unobserved shocks which are correlated over time and therefore
induce serial correlation in the error term. For instance, a firm-country combination is
hit by a positive shock in one year which pushes the firm into that market. In the next
period the firm realizes that the shock returns to its mean implying negative profits from
exporting to this market so that the firm exits again. This mean reversion of the shock
may lead to negative correlation in the error process if the firm believes that the shock
remains at the new level. The estimation results presented in the next section are based
on a model which allows for both implications.
4
4.1
Estimation Results
Non-linear Models
In Table 7 I present estimation results for the non-linear model on the balanced panel.
In the upper part of the table I present parameter estimates and test statistics and in
the lower part of the table average partial effects (APE) are presented to evaluate the
economic meaning of the coefficient estimates. In column (i) I estimate the model without
considering an AR1 process in the error. The results clearly point towards the importance
of sunk costs of exporting also with respect to individual markets. The APE of the sunk
20
costs parameter suggests that a firm that has exported last year to market d is 34% more
likely to export to d today than a firm that has not exported to d in the previous year.
Having last exported to market d two or three years ago also significantly increases the
probability of exporting to d today, while the APEs are much smaller. The other coefficient
estimates in column (1) suggest that more productive and larger firms are more likely to
export to a market and that firms in Denmark export to relatively developed, small and
nearby markets. Bilateral exchange rate movements do not matter significantly which
may be explained by the high degree of product differentiation in this sector which makes
firms less dependent on changes in exchange rates. Moreover, the estimate of λ suggests
that roughly one third of the error variance is due to the time-constant error component.
Note that the number of observations is 52,470 where 17,490 refer to the three pre-sample
years and 34,980 to the sample years.
In column (ii) I allow for an AR1 error process. δ is estimated to equal -0.35 implying
significant negative serial correlation in the transitory error component. As a consequence,
the importance of sunk costs is underestimated in column (i) where δ is neglected. This
can be seen by comparing the APEs of lagged export status in columns (i) and (ii); when
accounting for δ, the APE increases from 34% to 47%. One explanation for the negative
serial correlation in the error term may be that firms believe that a positive shock to
the firm-country combination leads to entry of competitors in that market. This would
be equivalent to the ambivalent effect of market size on exports in the model of Melitz
and Ottaviano (2008). The authors show that the sign of the effect of market size on
exports depends on whether the market opportunity or the market competition effect
dominates. Equivalently, a shock e.g. to a foreign market’s terms of trade can give rise
to market opportunity or market competition effects while the results here suggest that
the latter dominates. Another explanation may be related to single year exporting firms
as suggested in the previous section.
In columns (iii) to (vi) I investigate the role of experience for exporting. I begin
by assessing the importance of general export experience from markets −d and import
experience from market d in year t − 1 for the decision to export to market d in t.
Both variables significantly increase the probability of exporting to market d today. In
21
particular, general export experience appears to be important being the second most
important predictor of current export status in market d. Import experience from market
d also matters significantly comprising the third most important predictor. Interestingly,
the role of lagged export status decreases significantly in column (iii) suggesting that
general and import experience indeed reduces the importance of country-specific sunk
costs. Comparing the APEs of lagged export status in columns (ii) and (iii) shows a
decrease by 36% indicating the economic importance of this effect.
The importance of general export experience may be explained by global sunk costs
of exporting which only have to be paid the first time a firm exports irrespective of the
market. The picture drawn by the transition matrix in Table 5 is in line with such an
explanation. Another reason why general export experience may matter is put forward
by Morales et al. (2011) who propose that firms export decisions with respect to different
markets are interdependent. I account for this by distinguishing the role of experience
from markets with characteristics similar to market d and experience from markets with
dissimilar characteristics. I use the common gravity variables to determine whether countries are similar; i.e. I consider two countries to be culturally similar if they speak the
same language or have a common colonial history and I consider two countries to be geographically similar if they share a common border or are located in the same region.23
The estimation results confirm that experience from markets with similar characteristics
is particularly valuable. The APE in column (iv) indicates that having last exported to
a market culturally similar to d increases the probability of starting to export to d today
by 3.1%. Column (v) shows that export experience from a geographically similar market
has an APE of 3.2%. Note that in either case the coefficient estimate on experience from
dissimilar markets remains statistically significant and economically important suggesting
that global sunk costs of exporting are indeed relevant.
As mentioned before, in the case that a firm’s export and import participation is
driven by similar unobserved factors, the lagged import variable is endogenous and may be
23
The geographic regions are: North-, East-, South-, West-, and Middle-Africa; Caribbean, North-,
Central-, and South-America; East-, South-, South-East-, West-, and Central-Asia; North-, East-, South, West-Europe; Oceania. Variables on language, colonial history and borders are taken from CEPII.
22
biased. I address this issue by jointly estimating a firm’s export and import participation
decisions using a bivariate dynamic discrete choice model. Remember that no AR1 process
is modeled here. Moreover, the 4-digit NACE dummy variables are dropped to speed up
the estimation process. The results presented in Table 8 suggest that firms’ export and
import decisions are indeed fairly similar. Except for productivity and foreign market
population, the variables in both equations behave similarly. Productivity is insignificant
in the import equation which may again be related to the specificities of this sector
where firms focus on the quality of their products. It is possible that more productive
high-quality producers have a larger share of the production process at home while less
productive firms rely more heavily on imports of low-quality components. The results
show that, equivalently to exporting, lagged import status in a market is the best predictor
for current import status in a market suggesting that importing is also characterized by
sunk costs. Moreover, general import experience and lagged export status matter for
current import status. The results further indicate that the error terms of both equations
are significantly positively correlated; this is particularly true for the time-constant error
components with a correlation coefficient of 0.44 (ρa ). Nevertheless, comparing the APEs
of lagged import status in the export equation in Table 8 with that in Table 7 suggests
that this correlation does not lead to an important bias as the effects are almost similar.
Overall, the results therefore suggest that importing and exporting can indeed be
explained by similar observable and unobservable factors. Moreover, when looking at the
APEs of the parameters for cross-equation state dependence (i.e. lagged export (import)
status in the import (export) participation equation), the model indicates that the effects
are of similar magnitude. This implies that importing from a market facilitates starting
to export there and vice versa. One explanation for these results may be that a firm
assembles knowledge about a market from selling to it which provides the firm with
information about potential suppliers for inputs or vice versa. Such an explanation is in
line with the common understanding that a large part of sunk costs is related to costs
of information gathering. An important drawback of this estimator is that it clearly
underestimates the role of destination-specific sunk costs of exporting as shown by the
average partial effect in the bottom of the table. This is the result of not allowing for an
23
AR1 process in the error component.
4.2
Linear Probability Model
To assess the robustness of the results, in Table 9 I repeat the estimation exercises from
Table 7 using a linear probability model. To ensure comparability to the previous results, I
estimate the models using the six years 2001 to 2006. In column (i) I estimate the model
using the one-step estimation approach and therefore neglect δ. I include four lags of
the dependent variable which all turn out to be highly significant. The other explanatory
variables loose significance which may be explained by efficiency losses from neglecting presample information in the estimation. The model passes the overidentification test, while
it fails the AR1 test implying that the instruments are invalid. I therefore turn to the twostep estimation approach described above where the AR1 error process is accounted for
by partially differencing the estimation equation and obtaining the structural parameter
estimates in a second step by minimum distance. In line with the non-linear model,
the AR1 parameter δ is estimated to be negative and significant. Note in particular
how similar also the magnitude of δ is in both cases. The test statistics for the first step
system GMM estimation confirm the validity of the model. As before, the results therefore
indicate that destination-specific sunk costs are underestimated when neglecting δ. In the
following columns (iii) to (v) the role of experience is investigated. Note that besides
the lagged dependent variable, also the experience variables are treated as endogenous in
the first step using GMM-style instruments. The results confirm the findings from before
that general export experience facilitates entry into new markets and that experience
from culturally and geographically similar markets is particularly valuable. The main
difference to the non-linear model is that the role of import experience is estimated to
be more important than general export experience. This may be related to endogeneity
of the import experience variable not accounted for in the non-linear model in Table 7.
While the bivariate model in Table 8 addresses the potential erogeneity of the import
variable, it neglects an AR1 error process in the export and import equations which may
result in an underestimation of cross-equation state dependence.
24
As the estimation results from the balanced sample may suffer from a selection bias
induced by only considering firms which exist during all 11 years of the sample period, I
check the sensitivity of the results by estimating similar models as before on an unbalanced
panel. One caveat, however, is that a balanced panel is required to allow for an AR1
process in the non-linear model. Therefore, I only use the linear probability model for
estimations on the unbalanced sample.
Estimation results are presented in Table 10. The one-step estimation approach in
column (i) does not pass the AR1 test at the 5% level so that the two-step approach is
again required. As before, δ is estimated to be negative and significant; the magnitude
of δ is only slightly smaller than before indicating the robustness of the estimates for
δ. Once the two-step approach is applied, the test statistics confirm the validity of the
results which are very similar to the results from before. The main difference is that
experience from culturally similar markets is estimated to be more important than experience from geographically similar markets on the unbalanced panel while experience from
geographically similar markets is estimated to be more important on the balanced panel.
I therefore conclude that the results presented in this paper are not driven by selection
effects or estimator choice.
4.3
Goodness of Fit
As a final exercise I assess the goodness of fit of the models. Two aspects are particularly
interesting here: First, to what extend does the predictive power increase from introducing
an AR1 process in the error? Second, to what extend does the predictive power increase
from additionally introducing gains from experience? I assess the models’ predictive
capabilities by comparing predicted and actual frequencies of firm export participation in
a given market. Moreover, I calculate Pearsons’ goodness of fit statistic while noting that
the statistic is supposed to act only as an informal summary of the models’ fit and not as
25
formal diagnostic.24 The statistic is obtained from
GoF =
S
X
ns − n̂s
s=1
n̂s
,
where ns and n̂s are observed and predicted frequencies of cell s.
Given the main sample period of six years, there are 26 = 64 possible trajectories of
firms’ export participation in one market. Many of these trajectories occur only with
very low frequencies which leads to a poor finite sample approximation of the asymptotic
distribution of test statistic (Hyslop, 1999). I therefore group the 64 frequencies into
6 categories based on firms’ export behavior in a market as also proposed by Roberts
and Tybout (1997). Table 11 presents the results; the upper part of the table refers
to the non-linear and the lower part to the linear model on the balanced panel. First,
consider the results for the non-linear model. When not allowing for an AR1 process,
the predictive power of the model is rather poor. The goodness of fit statistic improves
sharply when allowing for an AR1 process and it further improves when allowing for
gains from general export experience and import experience. Hence, allowing for an AR1
process is also important for the predictive capabilities of the model. This is confirmed
by the results for the linear probability model. As before, the fit of the model increases
sharply when allowing for an AR1 process. However, in case of the linear model, no
additional improvements in the fit of the model are observed from allowing for gains from
experience. Therefore, the AR1 structure appears to be an important factor in modeling
firms’ export behavior in individual markets.
5
Conclusion
This paper estimates the importance of country-specific sunk costs and pays special attention to the role that previous experience in international trade may have for foreign
market entry. In the model firms can benefit from experience of importing to a specific
24
See Hyslop (1999) for more details. Also note that no corrections for the estimation of k parameters
has been made.
26
market and from experience of exporting to other markets. The former point implies
that firms may collect foreign-market-specific knowledge from importing from a country
which can then help the firm to start exporting to it; e.g. by familiarizing the firm with
the foreign market’s conditions. General export experience may be relevant if sunk costs
of exporting consist of general and market-specific costs so that a firm does not have to
consider general costs again if it exported to some market in the previous year. Moreover,
export experience from other markets may be relevant as it can ease entry into markets
which are similar in some characteristics such as the language.
I motivate an empirical model which allows for all of these mechanisms. The importance of sunk costs is inferred from the degree of state dependence of firms’ export
participation in a market. Unlike other studies, I do not only allow for time-constant
unobserved heterogeneity in the error process, but also for an AR1 component. This complicates the estimation procedure which is why I resort to maximum simulated likelihood
estimations and a two-step approach involving GMM and minimum distance techniques.
Estimations are based on data from the furniture manufacturing sector in Denmark. This
sector is highly involved in international trade making it an interesting case to study. The
data is very rich in that it not only provides balance-sheet information, but also detailed
transaction-level data on firms’ exports and imports.
The results show that allowing for an AR1 error process is important for identifying
true state dependence. Country-specific sunk costs are substantially underestimated if the
AR1 process is neglected. Also the predictive power of the model improves sharply when
the AR1 process is introduced. The results further suggest that country-specific sunk costs
are indeed substantial; a firm that has exported to a market last year is 47% more likely
to export to this market today compared to a firm with no export and import activities
in the previous year. However, the importance of these costs is reduced significantly if the
firm has experience in international trade. Controlling for previous import and export
experience reduces the role of market-specific sunk costs by 36%. Export experience from
other markets is particularly important for explaining this result suggesting that sunk
costs of exporting can be distinguished into general and market-specific costs. If the firm
has previous export experience from a country with similar characteristics (e.g. language)
27
like the new one, export market entry is further facilitated. Moreover, the results show
that importing from a market can induce starting to export there. This suggests that
market-specific knowledge from importing eases export market entry. Results from jointly
estimating firms’ export and import participation equations show that the effect also exits
for the opposite direction.
Overall, this paper adds to our understanding of firms’ internationalization strategies
by depicting the role of firms’ experience in international trade and the interconnectedness
between their exporting activities in different markets on the one hand and their exporting and importing activities in the same markets on the other hand. Moreover, the paper
shows that there are unobserved factors which play an important role in firms’ exporting and importing decisions which require explicit modeling in order to obtain unbiased
parameter estimates.
Acknowledgements
I am grateful to Christian Bjørnskov, Shigeki Kano, Jan de Loecker, Alfonso Miranda,
Eduardo Morales, Steve Redding, Alejandro Riano, Frederic Warzynski, and to the participants at the 2011 annual meeting of the European Economic Association, at the 2011
Danish international economics workshop, at the 2011 annual GEP post graduate conference, at the 2012 NOITS workshop and the 2012 conference on international economics.
I acknowledge financial support from The Tuborg Foundation.
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32
6
Tables
Table 1: Sector 361 in global markets
Number of firms
Exports over sales
Imports over materials
Average no. of export destinations
Average no. of import origins
33
1998
2002
2006
278
0.36
0.21
6.44
2.89
231
0.28
0.21
6.88
4.11
165
0.26
0.22
6.70
4.59
Table 2: Exports by NACE 4-digit & imports by HS 2-digit
EXPORTS
NACE
4-digit
3611
3612
3613
3614
3615
Manufacture of
Chairs and seats
Other office and shop furniture
Other kitchen furniture
Other furniture
Mattresses
No. of
Firms
95
59
37
145
4
IMPORTS
HS
2-digit
44
94
83
41
39
48
73
52
70
99
Product Category
Wood and articles of wood; wood charcoal
Furniture, bedding, mattresses etc.
Miscellaneous articles of base metal
Raw hides and skins (other than furskins) and leather
Plastics and articles thereof
Articles of iron or steel
Paper and paperboard; articles thereof
Cotton
Glass and glassware
Reserved for special uses by contracting partners
34
Import in
Mill. DKK
5847
5251
937
723
609
400
371
310
194
192
ExportSales
0.39
0.20
0.14
0.39
0.26
Table 3: Main export destination and import origins (by mill. DKK of shipments)
Exports
DEU
SWE
NOR
GBR
USA
NLD
FRA
CHE
JPN
AUT
14414
4897
4538
3907
3219
1911
1814
1126
1096
1069
Imports
DEU
SWE
ITA
FIN
BEL
AUT
POL
THA
GBR
CHN
35
4714
3237
1404
1040
741
740
641
373
350
324
36
Unbalanced Sample
Log TFP (t-1)
Log No. of Employees (t-1)
Log GDP
Log Population
Change in Exchange Rate
Log Distance
First Exporter
First Importer
No. of Observations
Balanced Sample
Log TFP (t-1)
Log No. of Employees (t-1)
Log GDP
Log Population
Change in Exchange Rate
Log Distance
First Exporter
First Importer
No. of Observations
109,670
11.604
3.598
25.636
16.423
2.563
7.813
52,470
11.678
3.728
25.653
16.426
2.344
7.813
0.466
0.895
1.728
1.794
57.782
1.095
0.462
0.929
1.725
1.793
52.648
1.095
Whole Sample
Mean
St. Dev.
92,930
11.550
3.481
42,716
11.616
3.591
0.445
0.820
0.443
0.861
No-Trader
Mean St. Dev.
3,110
11.854
4.039
1,765
11.872
4.105
0.438
0.918
0.427
0.932
Importer
Mean St. Dev.
Table 4: Summary Statistics
9,202
11.871
4.184
5,190
11.921
4.272
0.471
1.012
0.459
0.974
Exporter
Mean St. Dev.
20.68%
6.32%
4,428
12.020
4.537
20.76%
6.45%
2,799
12.042
4.574
0.435
0.997
0.417
0.949
Two-Way-Trader
Mean
St. Dev.
Table 5: Transition matrices
EXPORTS
Market coverage in t-1
Markets in t
+ 4 or more
+ 3 Markets
+ 2 Markets
+ 1 Market
Unchanged
- 1 Market
- 2 Markets
- 3 Markets
- 4 or more
0
0.01
0.01
0.02
0.12
0.84
0.00
0.00
0.00
0.00
1
0.02
0.06
0.06
0.20
0.40
0.26
0.00
0.00
0.00
2
0.04
0.02
0.07
0.22
0.37
0.16
0.12
0.00
0.00
3
0.00
0.03
0.07
0.23
0.39
0.23
0.04
0.01
0.00
4
0.04
0.02
0.11
0.21
0.28
0.21
0.09
0.04
0.00
5
0.02
0.02
0.06
0.15
0.32
0.09
0.19
0.06
0.09
6 to 10
0.04
0.06
0.10
0.17
0.19
0.17
0.12
0.06
0.09
above 10
0.08
0.09
0.12
0.12
0.17
0.17
0.08
0.08
0.09
5
0.06
0.00
0.04
0.26
0.24
0.26
0.06
0.06
0.02
6 to 10
0.06
0.07
0.13
0.17
0.23
0.12
0.09
0.07
0.04
above 10
0.09
0.09
0.08
0.12
0.14
0.17
0.10
0.07
0.14
IMPORTS
Market coverage in t-1
Markets in t
+ 4 or more
+ 3 Markets
+ 2 Markets
+ 1 Market
Unchanged
- 1 Market
- 2 Markets
- 3 Markets
- 4 or more
0
0.01
0.01
0.02
0.14
0.82
0.00
0.00
0.00
0.00
1
0.04
0.03
0.03
0.17
0.50
0.23
0.00
0.00
0.00
2
0.05
0.05
0.10
0.13
0.24
0.29
0.13
0.00
0.00
3
0.08
0.03
0.05
0.13
0.24
0.21
0.21
0.05
0.00
37
4
0.09
0.09
0.11
0.26
0.26
0.09
0.04
0.06
0.02
Table 6: Firms that start exporting, stop exporting, continuously export and export a
single year to a market
Number of Firms
Total Export Volume (in mill. DKK)
Export Volume per Firm (in tsd. DKK)
Starters
Stoppers
Single Year
Continuous
149
108
675
129
33
245
133
13
98
1056
3468
3254
Numbers are time means over the sample period 1996-2006
38
39
0.474
0.024
0.036
0.467***
-0.354***
0.252***
3.567***
52,470
0.147
0.373***
0.385***
0.451***
-0.409***
-0.105***
0.0004
2.411***
0.303***
0.424***
(0.067)
(0.021)
(0.037)
(0.488)
(0.052)
(0.033)
(0.032)
(0.03)
(0.015)
(0.002)
(0.076)
(0.066)
(0.079)
(ii) AR1
0.018
0.349
0.012
0.018
0.027
(0.054)
(0.022)
(0.034)
(0.382)
(0.046)
(0.052)
(0.032)
(0.031)
(0.029)
(0.016)
(0.002)
0.388***
0.348***
0.321***
0.444***
-0.411***
-0.1***
0.0005
0.544***
-0.346***
0.239***
3.112***
52,470
0.161
(0.076)
(0.066)
(0.078)
(0.061)
2.318***
0.286***
0.395***
0.526***
0.343
0.011
0.016
0.032
0.021
0.013
0.031
0.022
0.013
0.531***
-0.345***
0.236***
3.516***
52,470
0.155
0.607***
0.454***
0.304***
0.328***
0.315***
0.452***
-0.425***
-0.085***
0.0006
2.302***
0.266***
0.367***
0.344
0.011
0.016
(0.063)
(0.022)
(0.036)
(0.473)
(0.065)
(0.062)
(0.044)
(0.052)
(0.032)
(0.031)
(0.029)
(0.016)
(0.002)
0.592***
0.464***
0.302***
0.329***
0.319***
0.424***
-0.399***
-0.089***
0.0004
0.539***
-0.342***
0.24***
3.457***
52,470
0.154
(0.077)
(0.066)
(0.079)
2.294***
0.269***
0.371***
(0.063)
(0.022)
(0.036)
(0.481)
(0.064)
(0.062)
(0.044)
(0.052)
(0.032)
(0.031)
(0.029)
(0.016)
(0.002)
(0.076)
(0.066)
(0.079)
GENERAL AND IMPORT EXPERIENCE
general & imports
cultural & imports
geogr. & imports
(iii) AR1
(iv) AR1
(v) AR1
All regressions contain year, 4-digit NACE industry, and region dummies; standard errors in parentheses ***, ** and * denote significance at the 1, 5 and 10 percent levels;
simulations based on 100 draws; Pseudo R-squared = 1-(LL(θ)/LL(0)); pre-sample parameter estimates and parameter on constant term omitted from table.
0.337
0.067
0.001
0.3***
4.226***
52,470
0.138
δ p (pre-sample)
δ(J + 1 . . . T )
λ
η
Number of Observations
Pseudo-Rsquared
Average Partial Effects
Lagged Export Status
Last Exported Two Years Ago
Last Exported Three Years Ago
General Export Experience (t-1)
Experience from Similar Market (t-1)
Experience from Dissimilar Market (t-1)
Import Experience (t-1)
(0.051)
(0.03)
(0.029)
(0.028)
(0.015)
(0.002)
0.377***
0.439***
0.521***
-0.469***
-0.115***
0.0004
(0.028)
(0.342)
(0.054)
(0.06)
(0.07)
1.86***
0.591***
0.256***
Lagged Export Status
Last Exported Two Years Ago
Last Exported Three Years Ago
General Export Experience (t-1)
Experience from Similar Market (t-1)
Experience from Dissimilar Market (t-1)
Import Experience (t-1)
TFP (t-1)
No. of Employees (t-1)
GDP
Population
Bilateral Distance
Bilateral Exchange Rate
(i) No AR1
NO GENERAL & IMPORT EXPERIENCE
Table 7: Non-linear model (MSL) on balanced panel
Table 8: Joint estimation of export and import participation
export equation
Lagged Exp / Imp Status
Last Exp/Imp Two Years Ago
Last Exp/Imp Three Years Ago
General Exp / Imp Experience (t-1)
Cross Equation State Dependence
TFP (t-1)
No. of Employees (t-1)
GDP
Population
Bilateral Distance
λ
ρa
ρν
Number of Observations
import equation
1.759***
0.546***
0.237***
0.722***
0.245***
0.217***
0.358***
0.499***
-0.432***
-0.236***
(0.059)
(0.061)
(0.071)
(0.061)
(0.063)
(0.049)
(0.029)
(0.03)
(0.027)
(0.021)
1.675***
0.521***
0.337***
0.516***
0.308***
0.066
0.25***
0.174***
0.008
-0.36***
(0.06)
(0.068)
(0.078)
(0.05)
(0.062)
(0.052)
(0.028)
(0.022)
(0.02)
(0.024)
0.338***
0.436***
0.242***
52470
(0.068)
(0.077)
(0.031)
0.248***
(0.076)
Average Partial Effects
Lagged Exp / Imp Status
Last Exp/Imp Two Years Ago
Last Exp/Imp Three Years Ago
General Exp / Imp Experience (t-1)
Cross Equation State Dependence
0.208
0.032
0.011
0.048
0.012
0.187
0.025
0.014
0.025
0.012
All regressions contain year dummies; standard errors in parentheses; ***, ** and * denote
significance at the 1, 5 and 10 percent levels; simulations based on 100 draws; pre-sample
parameter estimates and parameter on constant terms are omitted from table.
40
41
(0.007)
(0.007)
(0.008)
(0.007)
(0.000)
0.01
0.013
0.009
-0.009
0.000
34,980
0.019
0.368
δ(J . . . T )
Number of Observations
Test for AR1 in error (p-value)
Overidentification Test (p-value)
-0.323***
34,980
0.098
0.889
(0.016)
(0.004)
(0.002)
(0.002)
(0.002)
(0.000)
(0.016)
0.168***
0.009**
0.006***
0.0038
-0.005**
0.000
(0.016)
0.771***
(ii) AR1
(0.018)
(0.004)
(0.003)
(0.002)
(0.002)
(0.000)
0.07***
0.006
0.004
0.007***
-0.008***
0.000
(0.016)
(0.012)
0.026**
-0.311***
34,980
0.109
0.821
(0.017)
(0.018)
0.144***
0.736***
-0.311***
34,980
0.147
0.769
0.042**
0.027**
0.079***
0.004
0.002
0.004
-0.006**
0.000
0.144***
0.734***
(0.016)
(0.017)
(0.012)
(0.02)
(0.004)
(0.003)
(0.003)
(0.002)
(0.000)
(0.017)
(0.017)
-0.308***
34,980
0.128
0.950
0.032**
0.02*
0.071***
0.006
0.005*
0.008***
-0.01***
0.000
0.138***
0.728***
(0.015)
(0.014)
(0.012)
(0.02)
(0.004)
(0.003)
(0.003)
(0.002)
(0.000)
(0.018)
(0.017)
GENERAL AND IMPORT EXPERIENCE
general & imports cultural & imports
geogr. & imports
(iii) AR1
(iv) AR1
(v) AR1
percent levels; parameter on constant term omitted from table.
All regressions contain year and 4-digit NACE industry dummies; bootstrapped standard errors in parentheses (400 repl.); ***, ** and * denote significance at the 1, 5 and 10
(0.024)
(0.019)
(0.02)
(0.026)
0.464***
0.211***
0.115***
0.095***
Export Status (t-1)
Export Status (t-2)
Export Status (t-3)
Export Status (t-4)
General Export Experience (t-1)
Export Experience from Similar Market
Export Experience from Dissimilar Market
Import Experience
TFP (t-1)
No. of Employees (t-1)
GDP
Population
Bilateral Exchange Rate
(i) No AR1
NO GENERAL & IMPORT EXPERIENCE
Table 9: Linear model (GMM-minimum distance) on balanced panel
42
(0.004)
(0.005)
(0.006)
(0.005)
(0.000)
0.016***
0.013***
0.013**
-0.012***
0.000
55,660
0.030
0.085
(0.019)
(0.015)
(0.016)
(0.021)
0.464***
0.196***
0.104***
0.083***
-0.306***
55,660
0.077
0.061
(0.015)
(0.003)
(0.002)
(0.002)
(0.002)
(0.000)
(0.014)
0.166***
0.011***
0.004*
0.004***
-0.005***
0.000
(0.015)
0.773***
(ii) AR1
(0.018)
(0.003)
(0.002)
(0.002)
(0.002)
(0.000)
0.067***
0.007**
0.002
0.006***
-0.007***
0.000
(0.015)
(0.007)
0.023***
-0.291***
55,660
0.084
0.103
(0.015)
(0.018)
0.145***
0.738***
-0.289***
55,660
0.133
0.398
0.033***
0.023***
0.074***
0.006**
0.001
0.005**
-0.007***
0.000
0.141***
0.735***
(0.015)
(0.012)
(0.007)
(0.018)
(0.003)
(0.003)
(0.002)
(0.002)
(0.000)
(0.016)
(0.018)
-0.287***
55,660
0.116
0.371
0.041***
0.018**
0.064***
0.007**
0.002
0.009***
-0.01***
0.000***
0.134***
0.725***
(0.015)
(0.01)
(0.008)
(0.019)
(0.003)
(0.002)
(0.002)
(0.002)
(0.000)
(0.015)
(0.018)
GENERAL AND IMPORT EXPERIENCE
general & imports cultural & imports
geogr. & imports
(iii) AR1
(iv) AR1
(v) AR1
percent levels; parameter on constant term omitted from table.
All regressions contain year, 4-digit NACE industry, and region dummies; bootstrapped standard errors in parentheses (400 repl.); ***, ** and * denote significance at the 1, 5 and 10
δ(J . . . T )
Number of Observations
Test for AR1 in error (p-value)
Overidentification Test (p-value)
Export Status (t-1)
Export Status (t-2)
Export Status (t-3)
Export Status (t-4)
General Export Experience (t-1)
Export Experience from Similar Market
Export Experience from Dissimilar Market
Import Experience
TFP (t-1)
No. of Employees (t-1)
GDP
Population
Bilateral Exchange Rate
(i) No AR1
NO GENERAL & IMPORT EXPERIENCE
Table 10: Linear model (GMM-minimum distance) on unbalanced panel
Table 11: Goodness of fit
NON-LINEAR MODEL
Always non-exporter (nexp)
Begin as nexp, switsch once
Begin as nexp, switsch more than once
Always exporter (exp)
Begin as exp, switsch once
Begin as exp, switsch more than once
GoF
AR1 error process
Gains from experience
LINEAR PROBABILITY MODEL
Always non-exporter (nexp)
Begin as nexp, switsch once
Begin as nexp, switsch more than once
Always exporter (exp)
Begin as exp, switsch once
Begin as exp, switsch more than once
GoF
AR1 error process
Gains from experience
43
Actual
frequencies
0.760
0.029
0.056
0.095
0.035
0.025
Actual
frequencies
0.760
0.029
0.056
0.095
0.035
0.025
Predicted frequencies
0.814
0.019
0.039
0.077
0.030
0.021
131.443
No
No
0.780
0.024
0.050
0.089
0.034
0.023
17.494
Yes
No
0.777
0.025
0.051
0.089
0.034
0.023
12.143
Yes
Yes
Predicted frequencies
0.797
0.025
0.037
0.092
0.028
0.021
85.741
No
No
0.757
0.030
0.061
0.094
0.035
0.024
2.154
Yes
No
0.757
0.030
0.061
0.094
0.035
0.024
2.154
Yes
Yes
A
TFP Estimation
The literature on productivity estimations provides different approaches for obtaining
TFP (see van Beveren (2012) for a recent survey). In this paper, I follow the structural
approach suggested by Wooldridge (2009). Wooldridge (2009) extends the existing twostep approaches of Olley and Pakes (1996) and Levinsohn and Petrin (2003)(henceforth
LP) by suggesting a more efficient one-step GMM alternative. The logic of this approach
is similar to that of LP while it does not suffer from the shortcomings of the two-step
approaches related to ignoring contemporaneous correlation in the errors across the two
equations and inefficient handling of serial correlation or heteroskedasticity. Estimation
is based on the following production function for firm i in year t
yit = η + βlit + γkit + εit ,
where y is the log of value added, η is a constant term, l is the log of employed labor,
and k is the log of capital stock. εit is the error term which consists of a firm-specific
time-varying component αit and a transitory shock ωit which is conditional mean independent of current and past inputs. αit is controlled for by a proxy variable approach.
In particular, it is assumed that for some function g(·), αit = g(kit , mit ), where mit is a
vector of proxy variables (here, following LP), intermediate inputs25 ). The conditional
mean independence assumption of ωit implies that
E(ωit |lit , kit , mit , li,t−1 , ki,t−1 , mi,t−1 , . . . , li1 , ki1 , mi1 ) = 0,
where serial correlation in ωit is allowed for as neither past values of yit nor of ωit appear in
the above assumption. Moreover, following LP, Wooldridge (2009) restricts the dynamics
in the productivity process (αit ) by assuming E(αit |αi,t−1 , . . . , αi1 ) = E(αit |αi,t−1 ) for
t = 2, 3, . . . , T and that kit is uncorrelated with the innovation ait = αit − E(αit |αi,t−1 ).
Wooldridge (2009) further points out that consistency also requires that ait is uncorrelated
25
Intermediate inputs or materials are obtained from the difference of turn over and value added.
44
with (ki,t−1 ,mi,t−1 ) which is ensured by imposing the condition
E(αit |kit , li,t−1 , ki,t−1 , mi,t−1 , . . . , li1 , ki1 , mi1 ) = E(αit |αi,t−1 ) = f [g(ki,t−1 , mi,t−1 )]
for given functions f (·) and g(·). Plugging αit = f [g(ki,t−1 , mi,t−1 )] into the production
function above gives
yist = η + βlit + γkit + f [g(ki,t−1 , mi,t−1 )] + ωit ,
which can be estimated by GMM approximating f (·) and g(·) by low-degree polynomials.
In the estimation, kit , ki,t−1 and mi,t−1 act as their own instruments and li,t−1 acts as an
instrument for lit . TFP values are then obtained from TFPit = yit − βlit − γkit .
B
Minimum Distance Estimator
Cameron and Trivedi (2005) point out that minimum distance estimation can be used to
estimate the structural parameter vector θ which is a specified function of the reduced
form parameter vector τ if a consistent estimate τ̂ of τ is available. In the current setup,
τ̂ is the parameter vector obtained from system GMM estimtion of equations (5) and (6)
in a first step. Denote q the number of structural parameters and r > q the number of
reduced form parameters and let the relationship between the reduced form and structural
parameters be given by τ0 = g(θ0 ). Note that it is not possible to use the estimator
θ̂ such that τ̂ = g(θ̂) since q < r. However, the minimum distance estimator θ̂M D is
available which instead minimizes the following objective function
Q(θ) = (τ̂ − g(θ̂))0 W(τ̂ − g(θ̂)).
W is a r x r weighting matrix. In particular, W = V̂(τ̂ )−1 , where V̂(τ̂ ) is the estimated
variance-covariance matrix of the reduced form parameter vector. The literature refers to
this estimator as optimal minimum distance estimator (Cameron and Trivedi, 2005).
45
C
Results with 100 and 250 draws
In Table C.1 I present estimation results for the baseline MSL model with AR1 error
process based on 100 and 250 draws. The results indicate that coefficient estimates are
very similar in both columns. In particular, the results for the coefficient of interest on
lagged export status as well as it’s average partial effect is hardly affected from increasing
the number of draws.
Table C.1: Baseline estimations of MSL model with AR1 error
100 draws
250 draws
Lagged Export Status
Last Exported Two Years Ago
Last Exported Three Years Ago
TFP (t-1)
No. of Employees (t-1)
GDP
Population
Bilateral Distance
Bilateral Exchange Rate
2.411***
0.303***
0.424***
0.377***
0.439***
0.521***
-0.469***
-0.115***
0.0004
(0.076)
(0.066)
(0.079)
(0.051)
(0.03)
(0.029)
(0.028)
(0.015)
(0.002)
2.415***
0.299***
0.421***
0.379***
0.39***
0.454***
-0.408***
-0.107***
0.0004
(0.076)
(0.066)
(0.079)
(0.052)
(0.033)
(0.032)
(0.03)
(0.015)
(0.002)
δ p (pre-sample)
δ(J + 1 . . . T )
λ
η
Number of Observations
0.467***
-0.354***
0.252***
3.567***
52,470
(0.067)
(0.021)
(0.037)
(0.488)
0.484***
-0.359***
0.253***
3.494***
52,470
(0.061)
(0.022)
(0.036)
(0.454)
Average Partial Effects
Lagged Export Status
Last Exported Two Years Ago
Last Exported Three Years Ago
0.474
0.024
0.036
0.473
0.023
0.035
All regressions contain year, 4-digit NACE industry, and region dummies; standard errors in
parentheses; ***, ** and * denote significance at the 1, 5 and 10 percent levels
D
Dynamic Discrete Choice Model with AR1 on Generated Data
In this appendix, I present estimation results from the MSL model with AR1 process
on simulated data. The data is generated as follows: α is generated from the standard
normal distribution implying that λ (=
α2
)
α2 +1
is equal to 0.5. The independent variables
x1 and x2 are generated from the uniform distribution on the intervals [-0.5, 0.5] and [1/3,
46
1 1/3], respectively. The instrument (Instt1 ) is generated from the uniform distribution
on the interval [0, 1] and the transitory error component is generated from the standard
normal.
The actual parameter estimates are presented in the first column of Table D.1 In
columns (ii) to (iv), results are presented for 9000 observations. I particular, 9 time
periods are considered and the number of individuals is set to 1000. Equivalently to the
models estimated in the paper, three periods are used for the pre-sample equation and
six periods for the main equation. The parameters of interest (i.e. the lagged dependent
variable and δ) are highlighted (bold) in the table. In column (v) I increase the number of
individuals to 5830 while still considering 9 time periods. The data set is therefore directly
comparable to the one used for estimations in the paper. Moreover, as in the paper, 100
draws are used for estimations. The results indicate that the estimator performs well.
Table D.1: Dynamic discrete choice model with AR1 on generate data
(i)
Actual
Coeff
Initial values
x1
x2
Inst t1
cons
Main equation
ly1
x1
x2
cons
δ p (pre-sample)
δ(J . . . T )
λ
θ
Observations
(ii)
50 draws
Coeff StE
(iii)
100 draws
Coeff StE
(iv)
250 draws
Coeff StE
(v)
100 draws
Coeff StE
0.5
-5
0.5
3
0.64
-4.83
0.32
2.95
(0.11)
(0.17)
(0.11)
(0.13)
0.50
-4.86
0.51
2.91
(0.11)
(0.17)
(0.11)
(0.13)
0.35
-4.68
0.45
2.84
(0.11)
(0.16)
(0.11)
(0.12)
0.54
-4.83
0.54
2.86
(0.05)
(0.07)
(0.05)
(0.05)
2
1.5
-5.3
2.5
0.4
-0.3
0.5
0.2
2.01
1.40
-5.27
2.44
0.38
-0.28
0.49
0.07
(0.11)
(0.11)
(0.21)
(0.12)
(0.05)
(0.06)
(0.03)
(0.05)
2.07
1.37
-5.42
2.55
0.34
-0.29
0.50
0.18
(0.1)
(0.11)
(0.21)
(0.13)
(0.06)
(0.05)
(0.03)
(0.05)
2.07
1.56
-5.49
2.54
0.32
-0.33
0.51
0.17
(0.11)
(0.12)
(0.24)
(0.13)
(0.05)
(0.06)
(0.03)
(0.05)
2.00
1.50
-5.22
2.45
0.31
-0.29
0.48
0.16
(0.04)
(0.05)
(0.09)
(0.05)
(0.02)
(0.02)
(0.01)
(0.02)
9000
9000
47
9000
52470
E
Bivariate Dynamic Discrete Choice Model on Generated Data
In the following, I present estimation results from the MSL model for a bivariate dynamic
discrete choice model. The actual parameter estimates are presented in the first column
of Table E.1 The number of individuals is set to 1000 and 9 time periods are considered.
In column (v) 5830 individuals are considered. Equivalently to the models estimated in
the paper, three periods are used for the pre-sample equation and six periods for the
main equation. The parameters of main interest are highlighted (bold) in the table; these
are the lagged depended variables, the variables for cross equation state dependence and
the correlation coefficients for the individual specific effects (α) and the transitory error
component (ω) in the main equations. The data generating process is as follows: The
independent variables x1 and x2 are generated from the uniform distribution on the intervals [-0.5.0.5] and [1/3,1 1/3], respectively.
The individual specific components (a1 , a2 ) are generated from the standard normal bivariate distribution with correlation 0.5.
The transitory error components in the initial period (ξ1 , ξ2 ) and the main equations
(ω1 , ω2 ) are generated from the standard normal bivariate distribution with correlation
0.4 and 0.3 respectively.
The exclusion restriction for the initial period (Instt1 ) is generated from the uniform distribution on the interval [-3/4, 1/4]. The instruments for equations 1 and 2 (Insty1 , Insty2 )
are binary variables generated from the standard normal.
Initial Equations
∗
y11
= 4x1 − 4.5x2 + 3 + 0.2a1 + 0.1a2 + ξ1t − 1.5Instt1 + 0.3Insty1
∗
y21
= −4.5x1 − 3.5x2 + 3 + 0.1a1 + 0.2a2 + ξ2t − 0.5Instt1 + 0.5Insty2
Main Equations
∗
y1t
= 0.6y1,t−1 + 0.2y2i,t−1 + 4x1 − 4x2 + 2.5 + a1 + ω1t + 0.1Insty1
∗
y2t
= 0.4y2,t−1 + 0.3y1i,t−1 − 4x1 − 3x2 + 2 + a2 + ω2t + 0.3Insty2
48
Table E.1: Dynamic bivariate probit on generated data
(i)
Actual
Coeff
Y1
Initial values
x1
x2
Inst t1
Inst y1
cons
Main equation
ly1
ly2
x1
x2
Inst y1
cons
Y2
Initial values
x1
x2
Inst t1
Inst y2
cons
Main equation
ly2
ly1
x1
x2
Inst y2
cons
ρa
ρξ
ρω
σa1
σa2
η1
η2
η3
η4
Observations
(ii)
50 draws
Coeff StE
(iii)
100 draws
Coeff StE
(iv)
250 draws
Coeff StE
(v)
100 draws
Coeff StE
4
-5.5
-1
0.2
2.5
4.30
-5.87
-1.22
0.19
2.67
(0.19)
(0.25)
(0.14)
(0.08)
(0.15)
3.94
-5.06
-0.93
0.43
2.12
(0.18)
(0.21)
(0.13)
(0.08)
(0.14)
4.18
-5.67
-1.09
0.28
2.61
(0.19)
(0.23)
(0.14)
(0.08)
(0.15)
4.02
-5.39
-0.94
0.23
2.44
(0.08)
(0.09)
(0.06)
(0.03)
(0.06)
2
0.2
4
-5
0.1
2.5
1.95
0.14
3.82
-4.70
0.13
2.31
(0.07)
(0.06)
(0.14)
(0.17)
(0.06)
(0.12)
1.91
0.23
3.72
-4.95
0.05
2.50
(0.07)
(0.07)
(0.14)
(0.17)
(0.06)
(0.12)
1.96
0.15
4.08
-5.01
0.04
2.54
(0.08)
(0.07)
(0.16)
(0.18)
(0.06)
(0.13)
1.97
0.25
3.96
-4.91
0.08
2.46
(0.03)
(0.03)
(0.06)
(0.07)
(0.02)
(0.05)
-4.5
-5
-0.5
0.5
3
-4.57
-5.09
-0.62
0.40
3.09
(0.18)
(0.19)
(0.12)
(0.07)
(0.14)
-4.53
-5.16
-0.52
0.50
3.11
(0.18)
(0.19)
(0.12)
(0.07)
(0.14)
-4.55
-5.13
-0.50
0.54
3.04
(0.18)
(0.19)
(0.12)
(0.07)
(0.14)
-4.42
-4.92
-0.42
0.50
2.97
(0.07)
(0.08)
(0.05)
(0.03)
(0.06)
1.5
0.5
-4
-4.5
0.3
2
0.5
0.4
0.3
1
1
0.2
0.1
0.1
0.2
1.49
0.50
-3.94
-4.51
0.10
2.19
0.53
0.52
0.26
0.91
1.05
0.16
0.14
0.20
0.09
(0.07)
(0.07)
(0.15)
(0.16)
(0.06)
(0.12)
(0.06)
(0.06)
(0.06)
(0.06)
(0.06)
(0.08)
(0.07)
(0.07)
(0.06)
1.41
0.46
-3.75
-4.24
0.13
2.04
0.54
0.37
0.31
0.96
0.94
0.19
0.06
0.17
0.15
(0.06)
(0.07)
(0.14)
(0.15)
(0.05)
(0.11)
(0.06)
(0.07)
(0.06)
(0.06)
(0.06)
(0.07)
(0.07)
(0.07)
(0.07)
1.45
0.52
-3.98
-4.35
0.00
2.08
0.50
0.34
0.27
1.04
1.02
0.15
0.13
0.08
0.26
(0.07)
(0.07)
(0.15)
(0.16)
(0.05)
(0.11)
(0.05)
(0.07)
(0.06)
(0.07)
(0.06)
(0.06)
(0.06)
(0.06)
(0.06)
1.52
0.51
-4.03
-4.47
-0.03
2.14
0.50
0.40
0.27
0.95
0.98
0.18
0.12
0.08
0.21
(0.03)
(0.03)
(0.06)
(0.07)
(0.02)
(0.05)
(0.02)
(0.03)
(0.02)
(0.03)
(0.03)
(0.03)
(0.03)
(0.03)
(0.03)
9000
9000
49
9000
52470