The Impact of the National Bank of Hungary's Funding

for Growth Scheme on Firm Level Investment∗

Marianna Endresz† Peter Harasztosi‡ Robert P. Lieli§

April, 2016

Abstract

The National Bank of Hungary (Magyar Nemzeti Bank, MNB) introduced a �fund-

ing for lending� type loan program aimed at small and medium sized enterprises (SMEs)

in mid-2013. We combine �rms' balance sheet data with two loan data sets to study the

program's impact on �rm level investment in 2013. We start from a simple di�erence-in-

di�erences (DID) estimator, but argue that the parallel trend assumption that underlies

the method is likely violated. Therefore, we propose a correction based on the idea that

the selection process involved in securing a market loan in a pre-program year is, in

some aspects, similar to the selection process into the program. Our results indicate

that the program succeeded in generating extra investment in the SME sector that

would not have taken place otherwise; speci�cally, we attribute to the program about

30% of the total investment undertaken by participating �rms. Nevertheless, the ef-

fect is markedly heterogeneous with respect to �rm size, being proportionally larger

for smaller �rms. A possible explanation for this �nding is that smaller SMEs were

initially more credit constrained on the market.

Keywords: funding for lending, program evaluation, investment, di�erence-in-di�erences esti-

mation, interactive �xed e�ects

JEL codes: D04, G38, E58

∗We thank Peter Bauer, Kristof Lehmann, Igor Masten, Daniel Palotai, Gabor Pellenyi, Adam Szeidl,Mihaly Szoboszlai, Viktor Varpalotai and Adam Zawadowski for their useful comments. A review by BalazsVonnak, in particular, led to substantial improvements. All remaining errors are our responsibility. At thetime the majority of this research was undertaken, all three authors had a�liations with the National Bankof Hungary. Nevertheless, the views expressed in this paper do not necessarily re�ect the o�cial views ofthe Bank.†The National Bank of Hungary. Email: valentinyinem@mnb.hu‡Joint Research Centre, Ispra. Email: peter.harasztosi@jrc.ec.europa.eu§Central European University, Budapest. Email: lielir@ceu.hu

1

1 Introduction

To facilitate recovery from the Great Recession, several central banks around the world have

taken on a more direct role in �rm �nancing in recent years. One of the better known such

programs is the Bank of England's Funding for Lending Scheme. The National Bank of Hun-

gary introduced its own Funding for Growth Scheme (Növekedési Hitelprogram; henceforth,

NHP) in June, 2013 with the purpose of reinvigorating the market for business loans and,

as was hoped, promoting economic growth through increased investment. As post-program

data starts becoming available, it is important to examine the extent to which these goals

have been met. In this paper we focus on �rm-level investment in 2013 as the outcome of

interest, and attempt to identify how much new investment the program has been able to

generate relative to an alternative universe without the program. This is a rather narrow

perspective that represents just one of many inputs a broader cost-bene�t analysis would

require.

The central bank allocated approximately EUR 2.33 billion (equivalent to 2.3% of Hun-

gary's GDP) to the �rst wave of the program.1 Commercial banks and other �nancial

intermediaries were entrusted with lending out these funds to SMEs at an interest rate not

exceeding 2.5% while bearing the risk of default.2 The policymaker also restricted the use

of the loan to four nominal purposes: (i) to re�nance existing loans; (ii) to �nance working

capital; (iii) to �nance new long-term investment; (iv) to pre-�nance EU funds. The �rst

wave of the program ended in September, 2013 after practically all funds were loaned out.

The program was extended almost immediately, but for administrative reasons the layout of

funds under the second phase was negligible for the rest of 2013. Thus, the 2013 investment

�gures we construct from �rm balance sheets re�ect the e�ect of the �rst wave only. Some

basic facts about the �rst phase of the program are summarized in Table 1.

The fundamental problem in evaluating the e�ect of the NHP program is that participat-

ing �rms cannot be regarded as a random sample from the universe of �rms. Comparing the

1All absolute monetary �gures reported in the paper are originally in 2013 Hungarian Forints (HUF). Forthe convenience of international readers, we converted most of these to euros at the exchange rate of 300HUF/EUR, roughly the prevailing exchange rate in 2013. E.g., EUR 2.33 billion ≈ HUF 700 billion.

2Eligibility for an NHP loan is tied to the o�cial EU de�nition of an SME. The most important constraintis that participating �rms cannot have more than 250 employees.

2

Table 1: Basic facts about the �rst phase of NHP

Firm size No. of No. of Part. Total loans Av. loan size(employees) �rms in 2013 participants rate (mill. EUR) (thsd. EUR)

Micro (1-9) 306,515 2,694 0.9% 633.9 235.3Small (10-49) 33,664 2,399 7.1% 690.2 287.7Med. (50-249) 4,442 826 18.6% 722.3 874.5N/A 55,738 203 0.4% 164.7 811.3

Total 400,359 6,122 1.5% 2211.1 361.2

Note: The table classi�es SMEs subject to double entry bookkeeping in Hungary in 2013. Extractedfrom the National Tax O�ce database. See Appendix B for additional details on the data.

average investment volume of participating �rms with non-participating �rms in 2013 reveals

a large gap between the two groups: EUR 225 thousand for the former vs. 15 thousand for

the latter. However, because �rms partly self-select into the program, and are also screened

by banks, it is not clear how much of this di�erence can be attributed to the program it-

self, and how much of it is due to systematic di�erences that would have led to di�erent

investment outcomes for NHP vs. non-NHP �rms even without the program. Alternatively,

making a before-after comparison, the mean real investment of participating �rms, measured

at 2013 prices, increased from EUR 156 thousand in 2012 to 225 thousand in 2013. It is

still not clear to what extent this change is due to the program, due to changes in general

economic conditions, or due to faster growing �rms self-selecting into the program. From

either perspective, identifying the program e�ect amounts to constructing the counterfactual

investment path that participating �rms would have been on in the absence of the program.

The simplest econometric method of program evaluation is to regress the outcome of

interest on a treatment dummy variable and a set of pre-treatment covariates (or some more

�exible function of them) using variation across �rms only. Less parametric versions of this

procedure, such as propensity score matching, still rely on the assumption that the set of

observed covariates is rich enough to control for all selection e�ects. While Endresz and

Harasztosi (2014) follow such a strategy in evaluating the e�ect of foreign currency lending

in Hungary on �rms' investment outcomes, in this paper we employ an identi�cation scheme

that also allows for some degree of unobserved heterogeneity.

3

More speci�cally, we start from a simple di�erence-in-di�erences (DID) estimator that

assumes participants and non-participants would have been on parallel investment paths

without the program. We point out however that this condition is unlikely to hold, and

propose a correction based on arguments that (i) selection into market borrowing in a pre-

program year is su�ciently similar to selection into the �rst phase of the program; and

(ii) that the relevant counterfactual for most participants is a market loan (presumably

smaller than the program loan). Technically, the average treatment e�ect of the program

for participating �rms is then estimated as the di�erence between two DID estimators.

While the proposed method is subject to a number of caveats, it serves as an example of

dealing with a situation where the parallel trend assumption, i.e., the additive separability of

individual and time �xed e�ects, is violated. In this sense, the paper is (distantly) related to

the econometric literature on interactive �xed e�ects (e.g., Bai 2009, Gobillon and Magnac

2015).

Our analysis relies on three data sources. The �rm panel of the National Tax and

Customs O�ce (Nemzeti Adó- és Vámhivatal, NAV) contains balance sheet data for all

Hungarian �rms with double entry bookkeeping obligations since the early 1990s. We use

this data set to construct �rm-level real investment and capital stock. Several other �rm

characteristics, such as number of employees, are also available in this data set. NHP loan

data are supplied on a mandatory basis to the National Bank of Hungary by mediating

banks. This information allows us to identify which �rms in the NAV database are NHP

participants, and what the o�cially stated purpose of each NHP loan is. Finally, we make

use of the Central Credit Registry, which can be matched with the NAV �rm panel up to

2011, to gain information about pre-program market borrowing. While the �rst data set

contains public information, the other two are only accessible through the central bank.

Hence, our results are not publicly replicable at present.

Qualitatively, our main �nding is that the program �works�, though its proportional e�ect

is very heterogeneous with respect to �rm size. On average, we attribute about 30% of the

total investment undertaken by participating �rms in 2013 to the program, but this ratio is

much larger for micro �rms (over 60%), and is e�ectively zero for upper medium-sized �rms.

4

Overall, we estimate that the program is responsible for about a 6% increase in investment

in the SME sector as a whole.

An important caveat in interpreting the numerical results is that new investment at

the �rm level does not necessarily correspond to an expansion of the capital stock in the

aggregate economy. For example, if �rm A has some old machinery with book value reduced

to zero, but �rm B buys it at a positive price, then we see an increase in �xed assets on �rm

B's balance sheet, but there is no disinvestment recorded on �rm A's. (Nevertheless, such

reallocation might lead to increased e�ciency in using existing capital.)

Lending or re�nancing programs focused on business credit have been implemented by

other central banks, for example, the Bank of England, but the ECB's (Targeted) Long

Term Re�nancing Operation ((T)LTRO) is also similar in spirit. While there has been some

e�ort directed at evaluating the impact of such loan programs (e.g., Churm et. al. 2012,

Darracq-Paries and De Santis 2013, van der Kwaak 2015, Balog et al. 2014, MNB 2014),

the analysis in these studies is based on aggregate data, and the focus is on credit market

outcomes, in�ation or output. Thus, both the results and the methodology of this paper are

of interest to researchers and policymakers outside of Hungary.

The study that is perhaps closest to ours is by Du�o and Banerjee (2014), who also use

�rm level data to analyze the e�ect of a directed lending program for small �rms in India.

Here we employ a highly simpli�ed version of their theoretical framework to rationalize the

size-related heterogeneity of the estimated program e�ect, which provides some insight into

the state of SME �nance in post-crisis Hungary. In particular, the results are consistent with

smaller �rms being initially more credit constrained on the market, and, at the same time,

larger �rms being rationed within the program.

The paper proceeds as follows. Section 2 describes the program evaluation framework

and lays out the identi�cation strategy in detail. Section 3 discusses the econometric imple-

mentation of the proposed estimator. We present the main numerical results in Section 4 and

provide possible interpretations in Section 5. Section 6 concludes. There are several Appen-

dices that describe the data in more detail (A-B), give supporting theoretical and empirical

analyses (C-D), and present results from variations on the main regression speci�cations (E).

5

2 The theoretical framework for evaluating NHP

2.1 Identi�cation strategy

We use the now standard potential outcome framework (e.g., Imbens and Wooldridge 2009)

to describe the parameter of interest and the identi�cation strategy. Let Y13(1) denote a

randomly chosen �rm's investment outcome in 2013 if participation in NHP were imposed

on it exogenously.3 Similarly, let Y13(0) denote the �rm's investment outcome if it were

exogenously excluded from NHP (or the program did not exist at all). Let P be the indicator

of program participation, i.e., P = 1 if a �rm participates in the �rst phase of NHP and

P = 0 if not. The relationship between the potential outcomes and the actually observed

investment in 2013, denoted Y13, is given by Y13 = PY13(1) + (1− P )Y13(0).

As participation in the program is voluntary, the average treatment e�ect for the treated

subpopulation (ATT) is of particular interest from a policy evaluation standpoint. Formally,

this treatment e�ect parameter is de�ned as

ATT = E[Y13(1) | P = 1]− E[Y13(0) | P = 1].

The counterfactual expression E[Y13(0) | P = 1] in the de�nition of ATT describes the hy-

pothetical average investment outcome of participating �rms in the absence of the program.

Obviously, this baseline is not estimable without further identifying assumptions. To moti-

vate these, we decompose the actually observed di�erence between the average investment

of participants vs. non-participants in the following way:

E[Y13 | P = 1]− E[Y13 | P = 0] = ATT + {E[Y13(0) | P = 1]− E[Y13(0) | P = 0]}

= ATT + {E[Y12(0) | P = 1]− E[Y12(0) | P = 0]}

+ {E[∆Y13(0) | P = 1]− E[∆Y13(0) | P = 0]}, (1)

3In our empirical models we use real investment volume (roughly, the change in �xed assets, intangibleassets plus depreciation) as the dependent variable, measured in millions of 2013 HUF, and converted tothousands of EUR in most discussions. In earlier versions of the paper we also considered models withinvestment rate as the dependent variable, but as the results are similar, we dropped them to simplify thepresentation. The estimated models will control for the capital stock directly and in a �exible way.

6

where Y12(0) is a randomly chosen �rm's potential investment in 2012 had NHP not been

implemented a year later, and ∆Y13(0) = Y13(0)− Y12(0).

One way to achieve identi�cation of ATT is to invoke the parallel trend assumption (e.g.,

Angrist and Pischke 2009, Ch. 5), which states that the average change in investment from

2012 to 2013 in the absence of the program would have been the same for participants and

non-participants alike. This implies that the second curly bracket in equation (1) is zero.

As the introduction of the program was not foreseeable in 2012,4 it is reasonable to further

assume that Y12(0) coincides with the actually observed investment outcome Y12. Under these

conditions, the ATT parameter is identi�ed by the di�erence-in-di�erences (DID) estimand

δ ≡ {E[Y13 | P = 1]− E[Y13 | P = 0]} − {E[Y12 | P = 1]− E[Y12 | P = 0]}. (2)

To illustrate identi�cation based on DID, Figure 1 shows investment volume in millions

of 2013 HUF for NHP vs. non-NHP �rms between 2010 and 2013. It is clear that partic-

ipating �rms, on average, invested signi�cantly more even before the program, but there

is still a marked uptick in investment among participants in the program year. As shown

by the dashed extension of the historical investment path for NHP �rms, the parallel trend

assumption amounts to claiming that in the absence of the program the 2012 di�erence in

average investment across the two groups would have prevailed in 2013 as well. The program

e�ect would then be given by the residual di�erence δ.

Figure 1 also shows that the investment di�erential between NHP and non-NHP �rms was

reasonably stable in the years leading up to the program, which seems to lend considerable

support to the DID approach. Unfortunately, this observation alone does not fully validate

the parallel trend assumption in the present setting. The reason for this is that the division

of the population into a treatment vs. control group is completely endogenous, i.e., a choice

made by �rms and banks, rather than the result of an exogenous �natural experiment�

as in the classic DID literature (e.g., Card and Krueger, 1994). Every year, even in bad

macroeconomic conditions, there are �rms that plan to increase their investment due to

4There was a change in management at MNB in the spring of 2013 and the identity of the new governorwas not known until shortly before. The new management announced the program within three months oftheir inauguration and proceeded with the implementation very quickly.

7

0

10

20

30

40

50

60

70

80

2010 2011 2012 2013

Avg I(t) in millions of 2

013 HU

F

non‐participantsNHP participantsDID counterfactual for participants

Effect by DID (δ)

Figure 1: The DID identi�cation strategy: average investment volume by participants andnon-participants

some favorable idiosyncratic �shock� (e.g., a good business idea, a positive shock to demand

faced by the �rm, etc.). It is realistic to assume that eligible �rms for which ∆Y13(0) is a

larger positive quantity are more likely to apply for a program loan. The reason is simple:

if it was worth it for a �rm to increase its investment in 2013 under market conditions, then

it was surely worth it under the conditions of the program. This argument implies that the

counterfactual mean investment path of NHP �rms in 2013 does not run parallel with that of

non-NHP �rms. Rather, NHP �rms would have likely been on a steeper path even without

the program as illustrated in Figure 2.

We propose a correction δ∗ to the basic DID estimator that attempts to capture this

additional selection e�ect. In essence, we assume that in the absence of the program the

average participating �rm would have used a combination of equity and market borrowing

to �nance some additional investment relative to the DID counterfactual, which represents

economic developments that a�ects participants and non-participants alike. The additional

investment relative to this path is estimated from the observed investment behavior of �rms

that borrowed on the market in a pre-program year. In particular, we construct a second

DID estimand, δ∗, where the treatment is now a market loan. In the remainder of this section

8

0

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20

30

40

50

60

70

80

2010 2011 2012 2013

Avg I(t) in millions of 2

013 HU

F

non‐participantsNHP participantsDID counterfactual for participantscorrection to DID counterfactual for participants

Correction (δ*)

Program effect (δ‐δ*)

Figure 2: Failure of the parallel trend assumption

we describe the mechanics of the proposed correction; additional discussion and supporting

evidence for the procedure will be provided in the next section.

Let P ∗t indicate whether or not a randomly chosen �rm took out a new market loan in

a given year t before the program and let Y ∗t (p), p = 1, 0, denote the potential investment

outcomes with and without market borrowing. Actual investment is again Yt = Y ∗t (1)P ∗t +

Y ∗t (0)(1− P ∗t ). Mimicking equation (1), we can write

E[Yt | P ∗t = 1]− E[Yt | P ∗t = 0] = ATT ∗ + {E[Y ∗t−1(0) | P ∗t = 1]− E[Y ∗t−1(0) | P ∗t = 0]}

+ {E[∆Y ∗t (0) | P ∗t = 1]− E[∆Y ∗t (0) | P ∗t = 0]}, (3)

where ATT ∗ is the average e�ect of a market loan on the investment volume of borrowing

�rms. Identifying Y ∗t−1(0) with the actually observed investment Yt−1, equation (3) shows

that the DID estimand

δ∗ ≡ {E[Yt | P ∗t = 1]− E[Yt | P ∗t = 0]} − {E[Yt−1 | P ∗t = 1]− E[Yt−1 | P ∗t = 0]} (4)

is the sum of the selection e�ect related to the slope of the planned investment path under

9

self-�nance plus the average treatment e�ect of a market loan on borrowing �rms, i.e.,

δ∗ = ATT ∗ + E[∆Y ∗t (0) | P ∗t = 1]− E[∆Y ∗t (0) | P ∗t = 0].

Hence, if we assume that �rms that chose to participate in NHP, or at least the majority

of them, would have borrowed on the market to �nance some investment even in the absence

of the program, we can take δ∗ as a proxy for E[∆Y13(0) | P = 1] − E[∆Y13(0) | P = 0] in

equation (1). In other words, we can identify the e�ect of the NHP program as the di�erence

between the two DID estimands δ and δ∗. In our empirical study we set t = 2011 as the

default correction year mostly for data availability reasons.5

To illustrate these ideas graphically, Figure 3 depicts sample analogs of the time series

E[Yt | P ∗11 = 1] and E[Yt | P ∗11 = 0] for t = 2007, . . . , 2011, i.e., the average investment path

of �rms that took out a new market loan in 2011 versus those that did not. Qualitatively,

Figure 3 is remarkably similar to Figure 1: (i) �rms that borrow on the market have a histor-

ically larger average investment volume; (ii) the investment di�erential between borrowing

and non-borrowing �rms is reasonably stable in the years leading up to the loan; and (iii) in

the loan year borrowing �rms exhibit a sizable uptick δ∗ in investment volume in excess of

this historical di�erence (as discussed above, we interpret this uptick as part selection, part

the treatment e�ect of the loan itself). The quantity δ∗ taken from Figure 3 is the correction

applied to the counterfactual investment path of NHP participants as shown in Figure 2.

2.2 Discussion of the correction term

Theoretical considerations The proposed correction is predicated on the assumption

that NHP participants would have been able to borrow on the market to �nance some

investment even in the absence of the program. (This rules out participants being completely

credit constrained in the sense of facing a vertical aggregate credit supply curve.) Of course,

5In estimating δ∗, one would ideally pick a year t with macroeconomic conditions similar to the programyear 2013. Unfortunately, we cannot use the closest pre-program year (t = 2012); as of compiling the data setfor this paper (October, 2014), the last year in which the central credit registry and the tax authority's �rmdatabase could be matched was 2011. Therefore we set t = 2011 in our baseline estimations, but examineearlier periods and the average of multiple periods as a robustness check; see Appendix E.1.

10

0

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30

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2007 2008 2009 2010 2011

Avg I(t) in millions of 2

013 HU

F

no new loan in 2011new loan in 2011DID counterfactual for firms with new loan in 2011

Correction (δ*)

Figure 3: Derivation of the correction term: investment by �rms with and without a newmarket loan in 2011

the program can still have a positive e�ect as participating �rms likely borrowed more under

the conditions of the program, and executed larger investment projects as a result. In essence,

part of the identifying assumption is that the program operates solely through the intensive

loan margin; the extensive margin e�ect is assumed to be zero. If the extensive margin e�ect

is non-negligible, i.e., there are many participants that would/could not have borrowed and

invested at all without the program, then the correction term will be too large.

A strong theoretical argument for participating �rms being already creditworthy is the

fact that the interest rate on a program loan is capped at 2.5%. This is less than the usual

risk premium banks charge to �nance most SMEs in Hungary, especially smaller ones (default

rates change inversely with size). As a result, banks likely cherry picked the best �rms from

their client base in dispensing the �rst wave of NHP loans, which is consistent with anecdotal

evidence we have from loan o�cers.6 In fact, one might well be worried about participating

�rms being more 'elite' investors than the average market borrower. Speci�cally, if those

6While the paper focuses strictly on the �rst phase of the program, we speculate that lending standardsgradually eased up with subsequent extensions. First, there was eventually so much money available thatbanks must have run out of elite �rms to lend to. Second, MNB later introduced a risk sharing scheme, whichallowed banks to share any future losses on program loans with MNB. Third, banks were arguably undersome political pressure to lend to diverse set of �rms. In fact, the introduction of the risk sharing schemecan be interpreted as a signal that the policy maker was not satis�ed with the initial program coverage.

11

�rms got selected into NHP for which ∆Y13(0) is exceptionally large, then the correction will

be too small.

The proposed correction also presumes similarity between macroeconomic conditions in

2011 (the baseline correction year) and 2013 (the program year). Unfortunately, there are

di�erences that might be of concern. For example, the central bank lowered interest rates

considerably between 2011 and 2013, suggesting that, other things being equal, the size

of an average market loan in 2011 might have been lower than the counterfactual market

loans that would have been taken out by NHP �rms in 2013 without the program. However,

when interest rates are high, it could also happen that only good �rms with larger investment

projects borrow, so the average loan size might actually be larger. The e�ect on the correction

term is therefore ambiguous.

In sum, there are a number of con�icting factors causing either upward or downward

bias in the correction term, and it is hard to judge their overall impact. In Appendix C

we present a very simple model that provides a theoretical framework for thinking about

selection into the program versus selection into market borrowing. The model is used to

illustrate the above mentioned sources of bias, and the ambiguity of their overall e�ect,

in a more structured and formal way. Therefore, it is also important to provide empirical

evidence in support of the proposed procedure.

Empirical evidence Firstly, the investment history of NHP participants already suggests

that these �rms may well have borrowed in the past (see again Figure 1). Clearly, the

average participating �rm invested consistently and substantially higher amounts than non-

participants for years before the program. Part of this is a size e�ect, but not entirely.

In Appendix A we reproduce the same picture for three di�erent �rm size categories and

obtain qualitatively similar results (moreover, the pattern persists if we look at the history

of the median investment rate). It is hard to imagine, perhaps some exceptions aside,

that such comparatively high levels of investment were sustainable without outside bank

�nance.7 Comparing Figures 1 and 3 shows that the average 2010 investment di�erence

7Alternative sources of outside �nance, such as a commercial paper or bond market, are basically non-existent for SMEs in Hungary. Investing from equity would be the only other option.

12

between NHP participants and non-participants (HUF 40 million) is in fact larger than the

corresponding di�erence between market borrowers and non-borrowers (HUF 35 million).

While the proposed correction does not need these pre-treatment level di�erences to be

the same, it does assume that in the absence of the program NHP �rms in 2013 would

have exhibited the same investment-uptick δ∗ relative to the investment path of non-NHP

�rms as did borrowing �rms in 2011 relative to the investment path of non-borrowing �rms.

We therefore further compare 2011 market borrowers and NHP participants based on a set

of pre-treatment characteristics, derived primarily from balance sheet data. As shown in

Table D.2.1 of Appendix D.2, the two groups appear reasonably similar in terms of most

variables except size. Speci�cally, NHP �rms tend to exceed even market borrowers both in

terms of initial capital and number of employees. Thus, we will allow δ and δ∗ to depend on

these size measures.

Secondly, but just as signi�cantly, we emphasize that for a subgroup of �rms there ex-

ists independent corroborating evidence showing that the correction to the baseline DID

estimator is well �calibrated� in magnitude. Speci�cally, as will be seen in Section 4, the

correction term (based on 2011 data) essentially eliminates the program e�ect among the

largest participating �rms (in the 150 to 250 employee range). Exploiting the participation

constraint that restricts program eligibility to �rms with 250 employees or less, it is possible

to conduct a fuzzy regression discontinuity analysis using �rms somewhat over the cuto� as

an exogenous control group. (These �rms are not used in any way in the corrected DID es-

timation.) This alternative exercise, presented in Appendix D.1, con�rms that the program

e�ect for the largest participating �rms is not signi�cantly di�erent from zero (in fact, the

point estimates are negative). While the result is, strictly speaking, speci�c to the group

of �rms close to the cuto�, it also enhances one's con�dence in the overall validity of the

correction idea.

Finally, in Appendix E.1 we examine the sensitivity of our baseline estimation results

presented in Section 4 to the choice of the time period over which the basic DID regression

and the correction term is estimated. We �nd that the most important numerical conclusions

are reasonably robust.

13

The supporting evidence notwithstanding, one might still remain somewhat skeptical

about whether the proposed correction is of the right magnitude for �rms of all sizes. Nev-

ertheless, the story of positive selection into NHP based on ∆Y13(0) is quite plausible, and

this fact alone implies δ∗ > 0. Therefore, results based on the uncorrected DID estimator,

which we will also report, can be regarded as an upper bound for the program e�ect.

3 Econometric implementation

The most direct implementation of the proposed estimator is based on sample analogs of the

expressions given in equation (2) and (4). Nevertheless, there are signi�cant advantages to

embedding these estimators into a regression model.

3.1 Regression speci�cation

Let Yit denote �rm i's real investment in year t, expressed in millions of 2013 HUF (or

thousands of 2013 EUR); see Appendix B.2 for the detailed de�nition. Let Pi = 1 if the �rm

participates in the �rst phase of NHP and is zero otherwise, and let Dxxt denote a dummy

variable that takes on the value one in year t = 20xx and is zero otherwise. The basic DID

estimand (2) can be consistently estimated under standard conditions by a two-period panel

regression of Yit on a �rm �xed e�ect, D12t, D13t (i.e., year �xed e�ects), and the interaction

of Pi and D13t for t = 2013, 2012; see Wooldridge (2002, Ch. 10). The estimated parameter

of interest is the regression coe�cient δ̂ on the interaction term.

Similarly, let P ∗i = 1 if �rm i has a new market loan in 2011 and zero otherwise. The

corrective DID estimand (4) can be estimated by an analogous two-period panel regression

for t = 2011, 2010 with P ∗i replacing Pi, D11t replacing D13t, and D10t replacing D12t.

Denoting the estimated regression coe�cient on the interaction term by δ̂∗, the simplest

version of the proposed ATT estimator is δ̂ − δ̂∗.

Taking these simple regression models as a starting point, we obtain our preferred re-

gression speci�cation by adding a number of features.

14

Allowing for treatment e�ect heterogeneity Firm size is an important covariate of

investment activity. We use the (real) capital stock (K) as well as number of employees (L)

as measures of �rm size.8 To some extent, �rm �xed e�ects control for level di�erences in

investment related to size (if size is persistent enough), but as mentioned in Section 2.2, it

is also important to allow for di�erential treatment e�ects by size. Therefore, we augment

the basic models with cubic polynomials of Ki,t−1 and Li,t−1 both in levels and interacted

with PiD13t or P ∗i D11t.9 We also examine some speci�cations that allow for treatment

e�ect heterogeneity with respect to industry, but as the aggregate results are not materially

a�ected, we only present these models in Appendix E.2 as part of our robustness checks.

Additional control variables We incorporate additional pre-treatment control variables

Xi,t−1 with both time and across-�rm variation into the regression models. Speci�cally, we

employ a number of �nancial statistics computable from a �rm's balance sheet (e.g., the

debt-equity ratio). The full set of controls is speci�ed in Appendix B.2; we also include

interactions between X and powers of K and L. Such controls help account for the pre-

treatment level di�erence in the investment activity of NHP vs. non-NHP �rms, and help

reduce estimated standard errors.

Final speci�cation Let β1(t), . . . , β4(t) be cubic polynomials in t ∈ R without a constant

term, and let B5(t) and B6(t) be vectors of such polynomials with dimension equal to the

dimension of X. Our preferred regression speci�cation is given by

Yit = ci + θ1D12t + θ2D13t + δPiD13t + β1(Ki,t−1 −K◦)PiD13t + β2(Li,t−1 − L◦)PiD13t

+ β3(Ki,t−1) + β4(Li,t−1) +X ′i,t−1γ +X ′i,t−1B5(Ki,t−1) +X ′i,t−1B6(Li,t−1) + uit, (5)

for t = 2013, 2012, where ci is the �rm �xed e�ect and uit is an idiosyncratic error, andK◦ and

L◦ are some reference level of capital and employment, respectively. An analogous regression

is estimated for the correction term over the period t = 2011, 2010 with P ∗i replacing Pi,

8Real capital stock is measured as the price-discounted value of �xed assets and intangible assets; seeAppendix B.2.

9Both capital stock and employment has enough time variation so that they can be included as a separatecontrols alongside a �rm �xed e�ect.

15

D11t replacing D13t, and D10t replacing D12t. Thus, δ̂ − δ̂∗ will give the estimated ATT

for �rms with capital stock equal to K◦ and employment equal to L◦.

3.2 Sample selection

The Tax and Customs O�ce �rm database contains the universe of all double entry book-

keeping �rms in Hungary every year from the early 1990s. (The data set has a panel struc-

ture, i.e., surviving �rms can be tracked across years.) Equation (5), and the corresponding

corrective regression, is estimated on a considerably smaller subset of �rms. We apply the

following screening procedures to obtain an estimation sample:

(i) We drop �rms that do not continuously exist between 2010 and 2013 or have missing

observations on K, L or X in one of these years. For the corrective regressions we

drop �rms that do not continuously exist between 2009 and 2011 or have missing

observations on K, L or X in one of these years. (We conduct robustness checks with

respect to the choice of the estimation period in Appendix E.1.) We further drop �rms

with investment volumes greater than EUR 100 million in absolute value to prevent

outliers from exerting an undue in�uence on the results.

(ii) To enhance covariate overlap between NHP participants and non-participants, we drop

a large number of barely active or non-active (mostly micro-size) �rms from the control

group that are very dissimilar from the majority of the treated in the following sense.

Using a probit regression, we estimate a treatment propensity score, i.e., the conditional

probability of program participation in 2013 given a constant and all the pre-treatment

control variables on the second line of equation (5). We then drop those �rms for

which this value is less than 0.35%, which amounts to approximately 79,000 �rms.10

A similar selection procedure is performed before estimating the corrective regression;

10This cuto� corresponds to the second percentile of the propensity score distribution for treated �rms,i.e., there are a few participants with propensity scores less than this value. Dropping or keeping thesetreated �rms does not make any meaningful di�erence. In fact, this entire �purging� of the control group hassurprisingly little e�ect on the numerical estimates. In previous working paper versions of this study (e.g.,Endresz, Harasztosi and Lieli 2015) we did not use this procedure and obtained very similar results.

16

the propensity score cuto� here is 0.15%, which means dropping about 62,000 non-

borrowers.

3.3 Benchmark matching estimator

Given the estimated propensity score for NHP participation, described in point (ii) of Section

3.2 above, one can easily construct matching estimators of ATT. We will report a simple

nearest neighbor version, where each NHP �rm is matched with the one control �rm that

has the closest propensity score value.

Such a matching estimator is consistent only if the selection-on-observables (unconfound-

edness) assumption is satis�ed, i.e., if (Y13(0), Y13(1)) is independent of P conditional on K12,

L12 and X12. Of course, we doubt that the set of observed covariates is su�cient for this

condition to hold; that is why we attempt to capture unobserved heterogeneity by com-

paring participants with market borrowers. Nevertheless, the matching estimator is still an

informative benchmark against which we can compare our method.

4 Estimation results

4.1 Average e�ects

Table 2 presents the estimated value of δ, the basic DID estimand, and δ∗, the correction for

self-selection related to the slope of the planned investment path, using the main speci�cation

described in equation (5). The reference level of capital and employment is the 2012 sample

average among participants; hence, the di�erence between δ̂ and δ̂∗ gives the average e�ect of

the program for a �representative� participant. As a benchmark, we also report the matching

ATT estimator described in Section 3.3. For ease of interpretation, the estimated investment

e�ect is also expressed as a percentage of the average 2012 capital stock among participants;

see the column labeled �I/K impact�.

Generally speaking, the estimation results show that the �rst phase of the Funding for

Growth Program did contribute to increased investment, i.e., �rms undertook investment

projects that they would not have undertaken in the absence of the program. Furthermore,

17

Table 2: Estimated average program e�ects for participants

Treatment=NHP participation

Model speci�cation Parameter estimates I/K impact(thousands of EUR) (% point)

δ δ∗ δ − δ∗ δ/K̄(δ−δ∗)

K̄

Matching 94.99 - - 10.2% -[15.83]

FE+f(K,L,X) 101.1 32.2 68.9 11.0% 7.5%[13.43] [18.97]

Note: For the �xed e�ects model, the reported estimates correspond to the2012 mean capital stock and employment among participants. Robust stan-dard errors are in brackets.

we see that the additional correction to the basic DID estimator makes an economically sig-

ni�cant di�erence. Speci�cally, the uncorrected DID estimate of the average program e�ect

is roughly 100 thousand euros per �rm, which reduces to 69 thousand after applying the

correction. The latter �gure corresponds to a 7.5 percentage point increase in the invest-

ment rate of the average participant. The matching estimator corresponds closely to the

uncorrected DID estimate. One the one hand, this similarity is not entirely surprising given

that equation (5) is fairly close to cross-sectional regression speci�cations that one could use

to estimate ATT under the unconfoundedness assumption. On the other hand, equation (5)

is a panel model that uses data from multiple years, so this correspondence is not automatic.

The estimated standard errors for δ̂ and δ̂∗ imply that the former estimate is individually

signi�cant at any conventional level, while the latter is just signi�cant at the 5% level (using

a one-sided t-test). The sum of the two standard errors provides an upper bound for the

standard error of δ̂ − δ̂∗, which is valid regardless of any possible correlation between δ̂ and

δ̂∗. Even this conservative approximation convincingly shows that the corrected estimate is

statistically di�erent from zero.

We will now turn to exploring the heterogeneity of the program e�ect as a function

of �rm size; more speci�cally, as a function of number of employees. (For most purposes,

employment gives information about �rm size in a more intuitive way than the capital

18

Table 3: Estimated average program e�ects by size category

Treatment=NHP participation

Size category Parameter estimates I/K impact(thousands of EUR) (% point)

δ δ∗ δ − δ∗ δ/K̄(δ−δ∗)

K̄

Micro (1-9) 80.67 5.00 75.7 19.9% 18.7%[9.33] [14.67]

Small (10-49) 95.67 31.33 64.3 11.2% 7.5%[12.67] [17.0]

Medium (50-149) 280.33 135.00 145.3 11.1% 5.8%[37.33] [56.67]

Medium (150-249) 308.67 273.33 35.3 6.0% 0.7%[109.33] [158.67]

Note: Estimates correspond to the 2012 mean capital stock and employ-ment among participants in each category.

stock.) We consider the standard size categories shown in Table 1 but split the medium

category into two subcategories (50 to 149 and 150 to 249). Given a size category c, let K̄c

and L̄c denote, respectively, the 2012 mean capital stock and mean employment level for

program participants in that group. Reestimating model (5) and the corrective regression

with K◦ = K̄c and L◦ = L̄c for each c, δ̂ − δ̂∗ gives the program e�ect evaluated at K̄c

and L̄c, and the corresponding standard errors are computed automatically. The results are

reported in Table 3.

The general message of Table 3 is that the impact of the program is proportionally

larger for smaller �rms. For micro �rms, the program e�ect on the investment rate is

18.7 percentage points (after correction), which is about two and a half times as large as

the overall proportional e�ect reported above (7.5 pp). At the other end of the spectrum,

the proportional e�ect practically disappears in the upper medium size category. Figure 4

provides an even more detailed picture, where the size categories are de�ned in much �ner

increments (note that the bins are not uniform ). Initially, the program e�ect falls at a

fast but decreasing rate, and stabilizes at around 30 employees on the 6-7 percentage points

level (roughly the overall average e�ect). We then see a further drop to zero and even into

19

‐10%

‐5%

0%

5%

10%

15%

20%

25%

1‐4

5‐9

10‐14

15‐19

20‐29

30‐49

50‐74

75‐99

100‐124

125‐149

150‐174

175‐199

200‐224

225‐249

investmen

t rate

The average proportional effect of NHP on participants

micro small  medium medium(1‐9) (10‐49) (50‐149) (150‐249)

Figure 4: The e�ect of NHP on investment rate as a function of employment

negative territory for the largest participating �rms. The individual standard errors reported

in Table 3 for δ̂ and δ̂∗ suggest that for the largest participating �rms, which is a relatively

small group, the di�erence δ̂ − δ̂∗ is unlikely to be statistically di�erent from zero.11

We emphasize that it is the estimated correction term δ̂∗ that �takes away� the estimated

program e�ect in the largest size category in Table 3�without it, the e�ect would be large

(EUR 309 thousand or 6.0 pp) and highly signi�cant. As mentioned in Section 2.2, there

exists independent corroborating evidence that the program e�ect is zero for the largest

participating �rms. In particular, one can compare �rms in a small neighborhood below

the employment ceiling of 250 with �rms in a small neighborhood above the ceiling. To the

extent that average �rm characteristics change gradually with size, the two groups should be

similar, except that the former is eligible for the program but the latter is not. If there is a

strong positive program e�ect, average investment activity should drop signi�cantly as one

crosses the eligibility cuto� from below. This regression discontinuity argument is developed

more formally in Appendix D.1; the results fully con�rm the lack of a program e�ect in

the largest size category. This shows that a correction to the basic DID estimator is indeed

11Indeed, the correlation between δ̂ and δ̂∗ would have to be close to perfect for the standard error of δ̂− δ̂∗to be lower than the point estimate of 35.3. This is the one point in the paper where computing standarderrors explicitly for δ̂ − δ̂∗ would add a bit more information, but it would be rather costly to design andimplement a bootstrap procedure just for this purpose.

20

Table 4: Decomposition of the actual investment by participating �rms in 2013

Investment (millions of EUR) Relative impact of NHP

Basic DID Corrected DID as % of all investment by:

actual w/o NHP due to NHP w/o NHP due to NHP participants SME sector

All �rms 1280.6 684.4 596.2 901.6 379.0 29.6% 5.7%

Micro (1-9) 279.0 88.6 190.3 102.8 176.2 63.2% 7.2%Small (11-49) 511.8 293.4 218.4 371.6 140.3 27.4% 6.3%Medium (51-149) 387.3 214.3 173.0 309.3 77.9 20.1% 6.4%Medium (151-249) 102.5 88.1 14.5 118.0 -15.4 -15.0% -2.1%

necessary, and increases the overall credibility of our empirical strategy.

That size is related to the program e�ect e�ect in an economically and statistically

signi�cant way is not surprising. For example, it is generally true that smaller �rms have a

larger average investment rate, albeit with a much larger dispersion. Moreover, the extent to

which the low interest rate on NHP loans changes the optimal level of capital can depend on

the pre-existing capital stock and employment level in a complex, nonlinear way, especially

when credit constraints are present. In Section 5 we will rationalize the observed size-related

heterogeneity of the program e�ect using simple credit demand and supply diagrams.

4.2 Aggregate e�ects: decomposing actual investment

To gauge the aggregate macroeconomic impact of the program, we construct individual

treatment e�ect estimates for each participating �rm in the estimation sample taking into

account the �rm's pre-program capital stock and employment level. Formally, for �rm i we

compute

δ̂ + β̂1(Ki,t−1 −K◦) + β̂2(Li,t−1 − L◦) (6)

and subtract o� the corresponding terms in the corrective regression (here K◦ and L◦ are

2012 sample averages among participants). We thus decompose the actual 2013 investment

volume of NHP -�rms into two parts: investment attributed directly to the program, and

residual investment, which would have been undertaken even in the absence of NHP.

21

The results of this exercise are collected in Table 4. As an upper bound for the aggregate

program e�ect, we also report the decomposition based on the uncorrected DID estimate, i.e.,

(6) alone, without subtracting the correction terms. The corrected estimate is highlighted

in bold. In the last two columns of Table 4 we compare this �gure to the total investment

volume of program participants and the full SME sector.

Taking the program as a whole, we �nd that about EUR 380 million out of the EUR

2046.4 million in NHP loans allocated to participants in the estimation sample was spent

on genuinely new investment, an 18.6% �conversion rate�. From a di�erent perspective,

this �gure amounts to about 30% of all investment undertaken by participating �rms, or

a 5.7% increase in the investment volume of the SME sector as a whole. (As a rule of

thumb, the SME sector in Hungary is responsible for about half of total private investment

in a year.) Size related treatment e�ect heterogeneity is again apparent. The proportion of

program-induced investment is well over 60% for micro sized �rms (EUR 176 million out of

279 million), while it drops to 20% in the lower-medium category (EUR 78 million out of

387 million). As estimates of the average e�ect have already shown, the program does not

meaningfully stimulate the investment activity of the largest participants. (The estimated

negative contribution of the program is due to the small number of observations and some

outliers in this category; see the regression discontinuity analysis in Appendix D.1 for a more

detailed look at upper medium size �rms.)

These �gures allow us to give a back-of-the-envelope estimate of the direct, �accounting�

impact on GDP of the �rst phase of NHP whilst ignoring any (or most) multiplier e�ects.

In particular, given the approximately 6/2 = 3 percent positive e�ect on total private in-

vestment, the investment share of GDP, and the fact that about half of total investment

is imports, we estimate that the program gave a 0.2% boost to GDP. This impact took

place already in 2013, over no more than a six month horizon. On the other hand, these

calculations still assume that all positive investment appearing on �rms' balance sheets is

an addition to the aggregate capital stock, which is rather optimistic.

22

5 Interpretation of the estimation results

We will use simpli�ed versions of the capital demand and supply graphs developed in Banerjee

and Du�o (2014, Section 3) as well as auxiliary data on program loans to rationalize the

size-related heterogeneity of the estimated program e�ect. The exercise o�ers insight into

the state of small business �nance in Hungary in 2013 and the channels through which the

program operates.

Figure 5(a) shows a �rm that is completely unconstrained on the credit market, i.e., it

faces a horizontal aggregate credit supply curve. This means that there is some �xed market

rate r∗ at which the �rm can borrow as much as it desires, which is the point K∗ where the

decreasing marginal product of capital becomes equal to r∗. If subsidized loans are made

available at the rate rnhp < r∗, the e�ect on capital will depend on how much the �rm is

allowed to borrow within the loan program. If the �rm is rationed, i.e., it can only borrow

some amount Lnhp < K∗ at the subsidized rate, then it will simply re�nance part of its

already existing capital stock and will not expand. Thus, for such �rms the program is

e�ectively a transfer. This situation is illustrated on Figure 5(b). In contrast, Figure 5(c)

shows that if the �rm is allowed to borrow as much as it wants at the subsidized rate, the

capital stock will increase from K∗ to Knhp as the marginal product of capital is downward

sloping.

At the other end of the spectrum, Figure 6(a) depicts a �rm that is completely credit

constrained on the market, i.e., it faces a vertical aggregate credits supply curve. This means

that no bank is willing to lend to this �rm at any price beyond the existing level of capital

K∗. If such a �rm can nonetheless borrow a small amount Lnhp within the program, then

this will be added to the �rm's capital stock; see Figure 6(b). In other words, the �rm

�rst expands, and will start re�nancing pre-existing capital only if it is allowed to borrow

su�ciently large amounts at the subsidized rate. If the �rm is entirely unconstrained within

the program, it will again end up with the level of capital Knhp shown on Figure 6(c).

In reality, most �rms likely face an intermediate situation where the aggregate credit

supply is upward sloping but not completely �at or vertical (in fact, the proposed correction

rules out NHP - �rms not being able to increase their borrowing at any price; c.f. Section 2.2).

23

(a)

capital

interest ra

te

capital supplyr*

K*

(b)

capital

interest ra

te

capital supplyr*

K*=Knhp

rnhp

Lnhp

(c)

interest ra

te

capital supply

r*

K*

rnhp

Knhp=Lnhp

Figure 5: The e�ect of a subsidized loan program on unconstrained �rms

24

(a)

capital

interest ra

te

capital supply

r*

K*

(b)

capital

interest ra

te

capital supply

r*

K*+Lnhp=Knhp

rnhp

Lnhp

(c)

interest ra

te

capital supply

r*

K*

rnhp

Knhp=Lnhp

Figure 6: The e�ect of a subsidized loan program on completely constrained �rms

25

In this case, a marginal subsidized loan dollar will be split between expansion (positive

program e�ect) and re�nancing (zero program e�ect) in a proportion determined by the

relative slopes of the capital demand and supply curves. The steeper supply is relative to

demand, the more will go toward expansion.

The foregoing discussion points toward a number of potential explanations for why we

observe a large proportional program e�ect for small �rms and no e�ect for large �rms. First,

smaller �rms may have been more constrained on the credit market before the program (i.e.,

they may have faced a relatively steeper aggregate credit supply curve). Second, even if all

�rms were originally unconstrained on the credit market, large participating �rms may have

been rationed within the program, while small �rms may have perceived it as unlimited once

they were cleared for the program by their bank. Finally, another theoretical possibility is

that all participating �rms were unconstrained both on the market and in the program, but

small �rms, on average, have more elastic capital demand curves.

Table 5 provides supplementary evidence for the �rst two stories. Column (1) shows the

ratio of NHP loan amounts with the �new investment� label to loans with the �re�nancing�

label in the four size categories used before. The ratio is as large as 128% for micro �rms

but falls below 50% in the medium categories. This pattern is consistent with smaller �rms

facing tighter initial credit constraints.12 As for the second channel, column (2) shows the

total value of all NHP loans taken out by participants as a fraction of their 2012 capital.

As can be seen, this ratio tends to be larger for smaller �rms, and the data show that some

micro and small �rms could actually borrow well in excess of their pre-program capital stock.

In contrast, in the two largest size categories the median program loan size is only about

25% of existing capital. This suggests that larger participants were indeed rationed within

the program (a less likely possibility is that they had limited access to even cheaper �nance

which they did not want to substitute for).

The fact that smaller �rms were allowed by banks to borrow more relative to their capital

12Note however that if a �rm originally faces a �at credit supply on the market, then the nominal purposeof its program loan is not necessarily informative. Suppose that the total amount the �rm can borrow underthe program is EUR 10, 000, a small amount relative to the �rm's capital stock. With a �at supply curve itdoes not matter whether the �rm uses the loan to re�nance the ��rst� 10, 000 euros worth of capital or the�last� 10,000, which is, say, due to a right-shift in capital demand in the program year. This last bit is thennominally a new investment project in 2013, but one that would have been implemented anyway..

26

Table 5: Types of NHP loans by �rm size

Firm size New investment loans Total NHP loansto re�nancing loans (%) to capital (%)

Average Median(1) (2)

Micro (1-9) 128 60Small (10-49) 82 31Medium (50-149) 49 25Medium (150-249) 41 26

Note: In column (2) we report the median as the average is distorted by some smaller �rms with very little

pre-existing capital receiving larger NHP loans.

is somewhat puzzling given that failure probabilities, and hence risk premia, are generally

negatively correlated with �rm size, and the 2.5% interest rate cap limits the risk premium

banks can charge. It is possible that smaller applicants were screened more selectively to

�t this reduced margin. A small �rm with a small default probability is then allowed to

borrow well in excess of its original capital because the absolute loan size and the expected

loss faced by the bank is still small.

6 Conclusions

By and large, our numerical results show that the National Bank of Hungary's Funding

for Growth Scheme succeeded in what was presumably one of its main goals�it generated

investment that would not have happened otherwise. A particularly robust feature of our

�ndings is that the program e�ect is heterogeneous with respect to �rm size with a larger

proportional e�ect for smaller �rms. On average, we attribute about 30% of the total

investment undertaken by participating �rms in 2013 to the program, but this e�ect is much

larger for micro �rms (63%) and vanishes for upper medium-sized �rms. From a slightly

di�erent perspective, additional investment induced by the program is estimated to boost

the average investment rate by about 19% points among participating micro �rms, 7.5%

points among small �rms, 6% points among lower medium-sized �rms and 0.7% points among

upper medium-sized �rms (technically, this last estimate is not signi�cantly di�erent from

27

zero). It seems that the largest participating �rms simply executed their already existing

investment plans for 2013�only cheaper, thanks to the program. This suggests that they

were facing an essentially �at aggregate credit supply curve on the market (i.e., were not

credit constrained), but were rationed with respect to the cheaper program loans.

More generally, the size-related heterogeneity of the proportional treatment e�ect is con-

sistent with the idea that smaller �rms were originally credit constrained (in the sense of

facing a steep aggregate credit supply curve), and that the program was helpful in easing

this constraint. However, the same �nding can be explained solely by small �rms being

unconstrained and larger �rms being rationed within the program, irrespective of any pre-

existing constraints on the market. Thus, no de�nite conclusions on this issue follow from

the evidence presented in this paper.

While our results suggest that the �rst phase of the Funding for Growth Scheme did

produce macroeconomic bene�ts through increased investment, a careful cost-bene�t analysis

is beyond the scope of the paper. Nevertheless, a few considerations that such an analysis

would require put the results further into perspective.

First, as explained in the introduction, positive investment at the �rm level does not

necessarily correspond to the creation of new capital in the aggregate economy�it can simply

signal a reallocation of the existing capital stock. (Such reallocation may still have a positive

e�ect on aggregate productivity.) Second, we do not have good qualitative information about

the type of investment projects undertaken. To use a simple but vivid example, we cannot

distinguish between a small bakery buying a picture to hang on the wall or buying a state-of-

the-art oven that allows them to bake pastries faster or in a more energy-e�cient way. Both

purchases result in an increase in �xed assets on the �rm's balance sheet, but it is of course

the latter that also increases potential output and is more conducive to long term growth.

Third, we do not yet know how the default rate on program loans is going to compare to

default rates on market loans. Fourth, we do not address in any way the opportunity cost

of the program. Fifth, analysis of the bene�t side could also be extended to include, say,

longer term employment e�ects.

In light of these caveats, there are several relevant directions for further research in the

28

evaluation of the program. Using the methodology of this paper, one could also estimate the

program e�ect on outcomes such as employment or sales. A well-executed survey could also

deliver important information about the type of investment projects undertaken. Subsequent

years will surely reveal more about dynamic and long term outcomes, including default rates,

though any data collected will also re�ect the additional impact of subsequent phases of the

program. This complicates the evaluation exercise because of the changing rules and possible

anticipation e�ects. It is our opinion that it will take several more years until well-founded

pronouncements can be made about the overall worth of the program.

29

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Card, D. and A. Krueger (1994). �Minimum Wages and Employment: A Case Study of

the Fast Food Industry in New Jersey and Pennsylvania.� The American Economic

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Churm, R., J. Leake, A. Radia, S. Srinivasan and R. Whisker (2012). �The Funding for

Lending Scheme.� The Bank of England Quarterly Bulletin, 2012 Q4, pp. 306-320.

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ECB's 3-year LTROs and the shift in credit supply.� ECB Working Paper Series, 1508,

January 2013.

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tion via Inverse Probability Weighted Estimators of (L)ATT� Journal of Business and

Economic Statistics, 32, pp. 395-415.

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ment. The Case of Hungary.� Emerging Markets Review, 21, pp. 265-287.

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Funding for Growth Scheme on Firm Level Investment.� Working paper, Magyar

30

Nemzeti Bank, 2015/2.

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31

Appendix

A. Historical investment of NHP and non-NHP �rms by size

020

4060

8010

0A

vg. I

(t)

Mill

ion

HU

Fs.

2009 2010 2011 2012 2013

a) all firms

020

4060

8010

0A

vg. I

(t)

Mill

ion

HU

Fs.

2009 2010 2011 2012 2013

b) micro-sized firms

020

4060

8010

0A

vg. I

(t)

Mill

ion

HU

Fs.

2009 2010 2011 2012 2013

c) small-sized firms

040

8012

016

020

0A

vg. I

(t)

Mill

ion

HU

Fs.

2009 2010 2011 2012 2013

d) medium-sized firms

Solid line: not NHP firms. Dashed line: NHP firms

Figure A.1: Mean investment volume by size (millions of 2013 HUF)

0.0

5.1

.15

.2.2

5M

ed. I

(t)/

K(t

-1)

2009 2010 2011 2012 2013

a) all firms

0.0

5.1

.15

.2.2

5M

ed. I

(t)/

K(t

-1)

2009 2010 2011 2012 2013

b) micro-sized firms

0.0

5.1

.15

.2.2

5M

ed. I

(t)/

K(t

-1)

2009 2010 2011 2012 2013

c) small-sized firms

0.0

5.1

.15

.2.2

5M

ed. I

(t)/

K(t

-1)

2009 2010 2011 2012 2013

d) medium-sized firms

Solid line: not NHP firms. Dashed line: NHP firms

Figure A.2: Median investment rate by size

32

B. Data appendix

B.1 Data sets, matching and sample selection

The �rm level data set used in this study is provided by the National Tax and Customs O�ce (NAV, formerly

APEH). It is comprised of the universe of double-entry book-keeping �rms subject to corporate taxation

in Hungary (we will call such �rms corporations). The data sources are corporate tax reports and balance

sheets submitted to the tax o�ce. The raw data set we compiled in October, 2014 gives full coverage of

corporations from 2007 to 2012 and close to full coverage in 2013.13

We match the �rm level balance sheet data with the data set on �rst-wave NHP participation, which also

includes the nominal purpose and the size of the loan taken out. This information is supplied to MNB on

a mandatory basis by mediating �nancial institutions. Table B.1.1 summarizes this data set along with the

result of the matching exercise. As the NHP scheme was also available for non-incorporated economic agents

(e.g. self-employed), there is a small fraction of program participants not contained in the NAV �rm panel.

For example, in the case of investment loans, EUR 35.3 million (about 6%) went to non-incorporated agents

out of the 584.7 million underwritten. For working capital �nancing and re-�nancing, the corresponding

�gures are 2.2 and 1.3 percent, respectively. At the same time, there are also a small number of NHP loans

that were received by corporations that cannot be identi�ed in the NAV database.14 Depending on the

loan type, we have not been able to match 2 to 4 percent of corporate NHP participants. In terms of loan

amounts, the proportion of loans going to unmatched �rms is similarly small.

Table B.1.1: NHP participation data by loan type in 2013 (millions of EUR)

Nominal purpose of loan: New investment EU pre-�nance Working capital Re�nanceNo. Amount No. Amount No. Amount No. Amount

All NHP loans 3231 584.7 53 4.3 2131 378.0 2755 1368.3Loans to not incorporated 576 35.3 12 0.7 162 8.3 151 18.3Loans to corporations 2655 549.3 41 3.7 1969 370.0 2604 1349.7Loans to corporations

identi�able in NAV database 2560 527.7 40 3.7 1910 362.3 2535 1317.4

Note: Loan amounts are in millions of 2013 EUR (converted from HUF at the exchange rate of 300 HUF/EUR).Total NHP loan amount is EUR 2335.3 million. Out of this, EUR 2211.1 million went to corporations identi�ed inthe NAV database, as given by the sum of the �gures in bold face. This is the loan total that appears in Table 1.The total number of loans is larger than the number of participating �rms reported in Table 1 as some �rms receivedmore than one type of NHP loan.

In Table B.1.2 we present the tax authority �rm data in more detail, and document how we arrive at

the estimation sample. Starting from the universe of corporations in 2013, we �rst drop those that are not

13The shortfall is due to �rms with non-standard accounting years and those that �led their reports withdelay. The proportion of such �rms is small; furthermore, a non-standard accounting year is typically chosenby large multinationals, not eligible for NHP anyway.

14Discrepancies can arise for multiple reasons. As mentioned in footnote 13, as of October 2014 the taxauthority database did not yet contain all �rms with reporting obligations for 2013. Other issues includemistyped identi�ers or consolidated balance-sheets.

33

Table B.1.2: Sample of �rms and NHP participants in 2013 - corrections in 2011

All Filter 1 Filter 2(availability/outlier) (prop. score)

dropped kept dropped keptPANEL A: Non NHP participants (2013)

Micro (1-9) 303,821 65,453 238,368 77,490 160,878Small (11-49) 31,265 4,696 26,569 1,395 25,174Medium (51-149) 3,001 150 2,851 23 2,828Medium (151-249) 615 35 580 20 560n.a. 55,535 55,535 0 0 0TOTAL 394,237 125,869 268,368 78,928 189,440

PANEL B: NHP participants (2013)

Micro (1-9) 2,694 127 2,567 0 2,567Small (11-49) 2,399 17 2,382 0 2,382Medium (51-149) 714 5 709 0 709Medium (151-249) 112 1 111 0 111n.a. 203 203 0 0 0TOTAL 6,122 353 5,769 0 5,769

PANEL C: No loan in 2011

Micro (1-9) 306,497 84,064 222,433 61,869 160,564Small (11-49) 27,105 4,957 22,148 540 21,608Medium (51-149) 2,494 201 2,293 26 2,267Medium (151-249) 464 42 422 14 408n.a. 47,195 47,195 0 0 0TOTAL 383,755 136,459 247,296 62,449 184,847

PANEL D: Loan in 2011

Micro (1-9) 19,472 519 18,953 0 18,953Small (11-49) 7,540 51 7,489 0 7,489Medium (51-149) 1,454 16 1,438 0 1,438Medium (151-249) 309 2 307 0 307n.a. 344 344 0 0 0TOTAL 29,119 932 28,187 0 28,187

Note: The table shows how we arrive at the estimation samples. Panels A and B show the sample of �rms used toestimate δ, while panels C and D display the sample for estimating δ∗. The column labeled 'All' shows the total numberof SMEs identi�ed in the tax authority data. The columns labeled 'Filter 1' show the number of �rms dropped vs. keptdue to data availability reasons or an outlier investment volume. The columns labeled 'Filter 2' count the number of�rms dropped vs. kept because of a low propensity score.

o�cially classi�ed as SMEs; the most important constraint is the cap on the number of employees (< 250).

The remaining �rms are broken down by size category and program status. These �rms constitute the 'raw

data' used potentially in estimating equation (5); see the column labeled 'All' in Panel A (non-participants)

and Panel B (participants). The number of �rms in this initial sample is 400,359; this is the set of �rms

displayed in Table 1. It can also be seen in Table B.1.2 that employment information is missing for a fairly

large subset of �rms; nevertheless, there is no strong reason to suspect that this is a non-random subset.15

15We have tried to improve size statistic availability by imputing employee data from nearby years (if avail-able) or using predicted values from a regression. The regression used to impute employment statistics con-tains sectoral average wage and total payroll as explanatory variables. Table B.1.2 presents after-imputation

34

The second �lter is data availability and outlier screening. In order to remain in the estimation sample,

a �rm must exist between 2011 and 2013, and the variables appearing in (5) cannot have missing values

throughout this period.16 Moreover, investment volume in 2012 and 2013 must be less than EUR 100 million

and greater than −100 million, which corresponds to a very high and very low percentile of the investment

volume distribution, respectively. The e�ect of these �lters is shown in the two columns labeled 'Filter 1',

both for non-participants (Panel A) and participants (Panel B). Finally, as described in Section 3.2, we

dropped those �rms for which the estimated propensity score, i.e., the program participation probability

conditional on the variables on the second line of equation (5), was below 0.35%.17 The number of �rms

dropped in this step and the �nal estimation sample is shown in the columns labeled 'Filter 2'.

To construct the estimation sample for the corrective regression, we �rst identify the �rms in the tax

authority database that increase their borrowing in 2011. This requires matching with the Central Credit

Registry. We then perform a cleaning procedure analogous to the one described above. Starting from the

universe of �rms in 2011, we apply the two �ltering steps, with the propensity score cuto� now set at 0.15%.

The sample sizes at the various stages are shown in Panel C (non-borrowing �rms) and Panel D (borrowing

�rms).

B.2 Variables

Investment volume and capital stock We de�ne real investment volume in year t as It =

(∆(FAt + IMMATt) +DEPRt)× IPI2013, where FAt and IMMATt are the end of the year stock of �xed

assets and immaterial (i.e., intangible) assets, respectively. DEPRt is the depreciation amount for year t and

∆ is the �rst-di�erence operator. IPI2013 is a NACE rev.2. 2 digit sector level investment price index that

is used to calculate real values of investments in 2013 terms. For newly created �rms (FA+ IMMAT )t−1 is

set to zero. The real capital stock in year t is calculated as the sum of FAt and IMMATt de�ated by IPI2013.

As discussed above, �rms with absolute investment volumes in excess of EUR 100 million are dropped from

the analysis.

Control variables (X) The vector X consists of the following �nancial and economic indicators:

equity, total assets, leverage, leverage share, return on assets, collateral, export share, liquidity. The de�ni-

tions and some descriptive statistics for these variables are collected in Table B.2.1. These statistics were

computed using all SMEs in the raw data set for which observations on the given variable are available in

2013. We also show NHP participants separately. These �gures reveal that NHP participants are larger in

terms of assets and equity, have lower leverage, and are more pro�table than the 'average' �rm.

�gures.16Recall that equation (5) is estimated for t = 2013, 2012; data availability in 2011 is needed because of

the lagged variables.17The propensity score model itself is estimated over the largest feasible sample of SMEs.

35

Table B.2.1: Firm level �nancial control variables in 2013

all �rms NHP �rmsvariable calculated as mean s.d. mean s.d.

equity equity (mill. HUFs) 66.3 1284 303.0 622.9

assets log of total assets (log of mill. HUFs) 3.09 1.8 5.29 1.7

leverage long+ short liabilities / total assets (%) 65% 83% 51% 28%

short leverage short /(short+long) liabilities (%) 85% 28% 76% 28%

return on assets pro�ts / assets (%) -3% 91% 9% 18%

collateral �xed assets / (�xed assets + immat.) (%) 1% 6% 1% 4%

export share share of exports in sales (%) 8% 25% 8% 20%

liquidity current assets / total assets (%) 66% 32% 51% 27%

Notes: This table lists the control variables used in equation (5). De�nitions are provided in column2 along with the unit of measurement (in brackets). Leverage, short leverage, collateral and exportshare variables are winsorized to lie between zero and one.

C. An illustrative structural model of �rms' borrowing

The economy is populated by a large number of heterogenous �rms and identical risk-neutral lenders (with

access to the world capital market). Capital, denoted by K, is the only factor of production, which �rms

need to borrow from a lender. While �rms are heterogeneous with respect to their default probability, and

this probability is also known by lenders, we make the (unrealistic) assumption that price-discrimination is

prohibited, and all lending is done at a given market rate rm, determined exogenously, say, by the rest of the

world. It is actually easy to solve the model with endogenous price formation and discrimination; the only

reason why we do not do this is that the ��x-price� solution will allow us to illustrate a richer set of selection

mechanisms without the need to add more complicated features. This is the only purpose of the model.

Firms need to pay a �x cost c > 0 to start operating. If a �rm chooses not to pay this cost, it remains

inactive and its payo� is zero. Active �rms draw projects, or more speci�cally, production technology at

random. With probability p, the �rm draws the production function f(K) = Kα, α ∈ (0, 1), and with

probability 1−p, production breaks down completely, output is zero and any capital borrowed by the �rm is

lost. (Such default events are independent across �rms.) Normalizing the price of output to unity, expected

pro�t for an active �rm is given by pKα − rmK, where we assume that �rms need to pay for their capital

regardless of whether the project is successful. Expected pro�t maximization then implies that the optimal

level of capital, if the �rm chooses to operate, is K∗ = (pα/rm)1

1−α , and the �rm chooses to operate i� the

36

success probability p satis�es

p >

(α

1− α

) 11−α c1−α

αrαm. (7)

The lender either accepts or rejects loan applications submitted by active �rms. If a �rm chooses to

be active, it will need to borrow the amount K∗. In case of rejection, the lender's payo� is normalized to

zero. If the lender approves an application, it will receive rK∗ regardless of whether the �rm's project is

successful, but it will lose all of K∗ if the �rm defaults (i.e., in this case the lender's payo� is (r − 1)K∗).

Expected pro�t maximization then implies that a loan will be approved i�

p > 1− rm. (8)

Characterizing borrowing �rms Suppose that �rms are heterogenous with respect to the success

probability p. Firm i will actually borrow if it chooses to become active and its loan application is approved.

Combining (7) and (8), this happens when

pi > max

{1− rm,

(α

1− α

) 11−α c1−α

αrαm

}≡ p(rm). (9)

Given the interest rate rm, the demand for capital for a �rm with default probability p can be written as

DK(p, rm) = K∗1(p > p(rm)).

Note that the r.h.s. of (7) is zero for rm = 0 and is increasing in rm. In contrast, the r.h.s. of (8) is one

for rm = 0 and is decreasing linearly in rm. It follows that p(rm) is generally a V -shaped function of rm,

i.e., the set of borrowing �rms can decrease or increase in response to changes in rm. More speci�cally, at

low interest rates it is the lender's participation constraint that is active, and a further decrease in rm will

reduce the set of borrowing �rms. On the other hand, if rm is large enough, then constraint (7) is active,

and a reduction in rm will increase the set of borrowing �rms. See Figure C.1.1.

We will model the introduction of the subsidized loan program simply as a reduction in the interest rate;

speci�cally, let rs < rm, where the subscript s stands for subsidized. Firms that borrow at rm will be called

market borrowers and �rms that borrow at rs will be called program participants.

Analysis of the proposed correction term In this model the ex-ante investment level di�erence

between borrowers and non-borrowers is zero, and investment by non-borrowers is further normalized to zero.

Thus, the observed average investment volume under the program corresponds directly to the δ parameter

in the empirical analysis, and the observed average investment volume under market conditions corresponds

37

Figure C.1.1: Selection into borrowing

to δ∗. More formally, let π(·) denote the distribution of the default probabilities pi. Then:

δ =

∫[p(rs),1]

DK(p, rs)π(dp)

/∫[p(rs),1]

π(dp),

and

δ∗ =

∫[p(rm),1]

DK(p, rm)π(dp)

/∫[p(rm),1]

π(dp).

Furthermore, de�ne

δ◦ =

∫[p(rs),1]

DK(p, rm)π(dp)

/∫[p(rs),1]

π(dp),

which is the counterfactual average investment volume of NHP participants that would have been realized

in the absence of the program (i.e., under rm). With these de�nitions, ATT = δ− δ◦, and the question is to

what extent this quantity can be proxied by δ− δ∗. We will now discuss potential sources of bias mentioned

in Section 2.2:

(i) Extensive margin e�ect. Suppose that p(rs) < p(rm), which means that, depending on the support

of π(·), there may be �rms that borrow in the program but not on the market. (This happens more

'easily' when, say, c is large or rm is large.) It is straightforward to show that δ∗ ≥ δ◦, i.e., the actual

38

average market loan under rm is larger than the average market loan for participants under rm, as

some participants borrow zero under rm. This implies overcorrection.

(ii) Program participants are too elite. Suppose that p(rs) > p(rm), which means that, depending on the

support of π(·), there may be �rms that could have borrowed at the higher market price but not in

the program. (This happens more 'easily' when, say, c is small or rm is small.) It is straightforward to

show that δ∗ ≤ δ◦, i.e., the actual average market loan under rm is smaller than the average market

loan for participants under rm. This implies to undercorrection.

(iii) Changing macroeconomic conditions. Suppose that the program reduces the interest rate from rm to

rs, but the correction (δ∗)′ is computed based on a year when the market rate r′m is larger than rm. In

this case (δ∗)′ may be larger or smaller than δ∗, and bias relative to δ◦ may be reduced or exacerbated.

(iv) Changing macroeconomic conditions. Suppose that the correction (δ∗)′ is computed based on a year

when the distribution of success probabilities π′ �rst order stochastically dominates π, i.e., economic

conditions are better. This results in (δ∗)′ > δ∗, but bias relative to δ◦ may again be reduced or

exacerbated.

39

D. Additional empirical evidence on the correction procedure

D.1 Regression discontinuity analysis

Here we consider investment volume as a function of the number of employees in a neighborhood of the

exogenous program eligibility cuto� (c = 250 employees). As participation for �rms below the cuto� is

voluntary and �rms above the cuto� are ruled out, the relevant design is fuzzy regression discontinuity with

one-sided non-compliance (see, e.g., Imbens and Lemieux 2008). Denoting the number of employees by L,

ATT for �rms with c = 250 employees is identi�ed by18

lim∆→0

E[Y13 | c−∆ ≤ L ≤ c]− E[Y13 | c ≤ L ≤ c+ ∆]

E[P | c−∆ ≤ L ≤ c]. (10)

In Table D.1.1 we show estimates of the numerator of (10) for various choices of ∆ (we also use neigh-

borhoods of c that are not symmetric around c). In each case we restrict the estimation sample to �rms

with number of employees falling into the given neighborhood. Due to the relatively small sample sizes,

outliers have a particularly large e�ect on this exercise. Therefore, we further drop �rms with large absolute

investment volumes; we report results for cuto�s equal to HUF 5 billion and 1 billion, respectively. We then

regress 2013 investment volume on a constant and the dummy variable Z = 1(L ≤ c). Thus, the estimated

slope coe�cient is the average investment volume of �rms below the cuto� minus the average investment

volume of �rms above the cuto�, restricted to the given neighborhood.

Table D.1.1: Estimates of the numerator of Equation (10)

Outlier cuto� HUF 5 billion HUF 1 billion

Empl. range 220-280 200-300 170-300 220-280 200-300 170-300

≤ 250 dummy -71.19 -75.29 -104.9 -8.039 -6.385 -31.29[79.38] [79.60] [70.92] [62.34] [47.42] [44.65]

Constant 196.4 344.2 344.2 196.4 199.0 199.0[69.60] [72.56] [67.58] [54.23] [43.17] [42.52]

Obs. 160 278 510 152 263 484

Note: The coe�cient estimates are in millions of 2013 HUF. Standard errors are in brackets.

As seen in Table D.1.1, the estimated slope coe�cients are negative throughout, which corresponds to a

18More generally, for a small ∆ > 0, the numerator of (10) divided by E[P | c − ∆ ≤ L ≤ c] − E[P |c ≤ L ≤ c + ∆] gives the average treatment e�ect for the subpopulation of �rms that (i) comply withthe intention-to-treat dummy Z = 1(L ≤ c), and (ii) have employees in the [c − ∆, c + ∆] range. This isa conditional version of the well-known LATE parameter of Angrist et al. (1996). However, because only�rms below the cuto� are eligible for the program (one sided non-compliance), and Z can be regarded ascompletely random in small neighborhoods of c, LATE coincides with ATT (see, e.g., Donald et al. 2014).

40

negative estimated program e�ect, especially with less strict outlier screening. However, the standard errors

are also large, so these point estimates are not signi�cantly di�erent from zero.19 Thus, there is absolutely

no evidence that average investment just below the cuto� is systematically larger than average investment

just above the cuto�.

Figure D.1.1 visually reinforces this �nding. The depicted �rms are in the [150,300] employee range,

covering the whole upper-medium size category, and absolute investment volume is capped at HUF 1 bil-

lion. NHP �rms are denoted by triangles, while non-NHP �rms are dots. Here we regress investment on

employment (rather than just a dummy) separately on both sides of the cuto�. Again, there is no evidence

whatsoever of a signi�cant discontinuity at the threshold; the con�dence intervals for the �tted regression

lines completely overlap.

-100

0-5

000

500

1000

i(t)

Mill

. HU

F

150 200 250 300Employment

confidence 95% below 250 fit above 250 fitInvestment NHP investment

Figure D.1.1: Investment by �rms in a neighborhood of the 250 employee cuto�

We note that this discontinuity analysis also passes the usual checks: there is no signi�cant bunching in

the 2013 �rm size distribution just below 2013, and we did not see discontinuities in any other pre-treatment

variables. Indeed as argued in footnote 4, the program was unanticipated and introduced quickly, so �rms

had little opportunity for strategic �rings to get below the eligibility threshold. (We are less sure about this

regarding subsequent extensions of the program.)

19If we keep the looser cuto� (HUF 30 billion) used in the rest of the paper, then we actually obtaintreatment e�ects that are negative and highly signi�cant.

41

D.2 Comparison of market borrowers and program participants

In Table D.2.1 we compare �rms that took out a new market loan in 2011 with �rst-wave NHP participants.

More speci�cally, we compare the (marginal) distribution of a number of investment-relevant covariates

across the following groups and years: (i) year 2010 values for �rms that took out any type of NHP loan

in 2013; (ii) year 2012 values for the same group of �rms; (iii) year 2010 values for �rms that took out a

new market loan in 2011; (iv) year 2012 values for the same group of �rms. The variables examined are

capital stock, number of employees, log assets, leverage, export share, return on assets, liquidity ratio, and

proportion of assets that can serve as collateral (see Table B.2.1 for more precise de�nitions).

Table D.2.1 shows that NHP participants are larger than market borrowers but their pre-treatment

balance sheet characteristics are otherwise reasonably similar (especially in 2010). There are relatively small

di�erences in terms of leverage (NHP participants are slightly less levered) and liquidity (NHP participants

are somewhat less liquid), and the rate of return attained by NHP �rms in 2012 is somewhat higher than

usual.

Table D.2.1: Some observed characteristics of NHP participants and market borrowers

NHP loan in 2013 Market loan in 20112010 2012 2010 2012

capital mean 2.57 2.93 1.39 1.55(100 mill. HUF) s.d. 5.97 6.35 12.33 10.72

median 0.74 0.89 0.12 0.17employment mean 23.22 23.76 13.55 14.05

s.d. 34.29 34.51 26.06 26.77median 10.00 11.00 5.00 5.00

assets mean 5.09 5.32 4.00 4.22(logs of mill. HUF) s.d. 1.77 1.67 1.80 1.77

median 5.18 5.40 3.89 4.11leverage mean 53.9% 51.1% 57.6% 60.7%

s.d. 35.0% 27.6% 39.4% 56.3%median 51.4% 49.8% 56.0% 54.0%

return on assets mean 6.6% 8.8% 6.4% 6.8%s.d. 25.2% 17.7% 40.0% 62.5%median 5.7% 6.4% 5.9% 5.0%

collateral mean 0.8% 0.9% 1.0% 1.1%s.d. 4.3% 4.5% 5.4% 5.7%median 0.0% 0.0% 0.0% 0.0%

export share mean 8.3% 8.1% 7.0% 7.2%s.d. 21.8% 20.4% 21.0% 20.9%median 0.0% 0.0% 0.0% 0.0%

liquidity mean 52% 51% 61% 60%s.d. 28% 27% 28% 29%median 51% 51% 64% 63%

42

E. Sensitivity analysis

E.1 Estimation periods

Here we examine how the estimation results delivered by our regression model change if we vary the years

included in the estimation period. In addition to the reported baseline of 2013-12, for the DID regression (5)

we consider 2013-2011, 2013-2010, and 2013-2009. For the corrective regression the baseline is 2011-2010; the

alternative periods considered are 2010-2009, 2009-2008, 2011-2009, and 2011-2008. In all cases we perform

a sample selection procedure analogous to that described in Section 3.2.

Table E.1.1 shows that estimates of δ are quite robust to the choice of the sample period. There is,

however, some variation in δ̂∗; e.g., the estimated value for the period 2011-2008 is about seventy percent

larger than the estimate for the baseline period (2011-2010). Subtracting the smallest δ̂∗ from the largest

δ̂ gives roughly EUR 84 thousand as the average treatment e�ect; at the other extreme, subtracting the

largest δ̂∗ from the smallest δ̂, we obtain about EUR 43 thousand as a lower bound. The chosen benchmark

estimation periods split this di�erence around the middle (a bit closer to the upper bound). In general, we

are rather wary of including the crisis years 2008 and 2009 in the estimation sample for the correction term.

Given data availability, this does not leave much room but to use 2011-2010 as the benchmark period.

Table E.1.1: Robustness of coe�cient estimates to choice of estimation period

equations for δ sample periods2013-2012 2013-2011 2013-2010 2013-2009

101.10*** 98.03*** 103.33*** 116.33 ***[13.43] [13.97] [14.23] [15.00]

equations for δ∗ sample periods2011-2010 2010-2009 2009-2008 2011-2009 2011-2008

32.20** 44.47*** 47.00*** 37.33*** 55.00***[18.97] [13.83] [15.00] [16.00] [14.33]

Note: Estimates are in thousands of 2013 EUR. Standard errors clustered by�rm are shown in brackets. (For two-year estimation periods these coincidewith 'regular' robust standard errors.)

Varying the estimation periods has very little bearing on the proportional program e�ect as a function

of size despite the variation in δ̂∗. In Figure E.1.1 we display four di�erent estimates of the proportional

ATT as a function of employment, corresponding to di�erent combinations of estimation periods for δ and

δ∗. It is reassuring to see that the estimates not only tell the same qualitative story but are also numerically

very close to each other.

Finally, we present robustness checks for the aggregate results. Table E.1.2 displays the estimated

aggregate e�ect of the program for every possible combination of the various estimation periods for δ̂ and

43

‐10%

‐5%

0%

5%

10%

15%

20%

25%

1‐4

5‐9

10‐14

15‐19

20‐29

30‐49

50‐74

75‐99

100‐124

125‐149

150‐174

175‐199

200‐224

225‐249

I(t)/K(t‐1)

DID:  2013‐2012 & Corr.:  2011‐2010 DID:  2013‐2012 & Corr. : 2011‐2009

DID: 2013‐2011 & Corr.:  2011‐2010 DID: 2013‐2011 & Corr. : 2011‐2009

Figure E.1.1: Sensitivity of the proportional program e�ect to the choice of the estimationperiod

δ̂∗. At �rst glance there appears to be a fair amount of variation, but this is mostly due to the three small

outliers in column three, where the corrective regression is estimate over the crisis years 2008-2009. If one

drops this column, the range of the estimates reduces quite substantially (EUR 353.32 million to 470.48

million). The reported benchmark e�ect (EUR 379.0 million) is closer to the conservative end of this range.

Table E.1.2: Robustness of aggregate e�ect in millions of EURs

CorrectionDID 2011-2010 2010-2009 2009-2008 2011-2009 2011-2008

2013-2012 378.96 353.32 269.90 358.76 358.762013-2011 406.79 381.15 297.73 386.59 386.592013-2010 413.47 387.83 304.41 393.27 393.272013-2009 470.48 444.83 361.41 450.28 450.28

minimum value is 269.90, maximum is 470.48

E.2 Sectoral heterogeneity

We also examine the sectoral heterogeneity of the treatment e�ect by augmenting the main speci�cation (5)

with interactions between sector dummies and PiD13t (P∗i D11t in the corrective regression). While some

of these interactions turn out to be statistically signi�cant, Table E.2.1 shows that the estimated aggregate

44

Table E.2.1: Aggregate program e�ect with and without sectoral heterogeneity (millions ofEUR)

actual w.o. NHP due to NHP % of actualTreatment = NHP participation

Main speci�cation 1280.57 901.61 378.96 29.6%

Main speci�cation + sectoral treatment e�ects 1280.57 937.06 343.51 26.7%

Note: The �rst row corresponds to the aggregate e�ects reported in Table 4.

program e�ect changes (drops) only by a small amount after adding this model feature.

Nevertheless, computing the aggregate program e�ect by sector shows that the two models are not always

in full agreement. As shown in Figure E.2.1, allowing for sectoral heterogeneity in the treatment e�ect

signi�cantly reduces the share of program-induced investment in the wholesale/retail sector and somewhat

reduces it in the construction services sector. This is counteracted by smaller increases in other sectors

(e.g., transportation, other services). In sum, exploring sectoral heterogeneity in more detail appears to be

a relevant direction for future research, but leaving it unmodeled does not seem to cause signi�cant bias in

the overall estimation results.

0

5

10

15

20

25

30

35

40

Agriculture, M

ining

Manufacturin

g

Electricity

, Gas, W

ater

Constructio

n

Retail, W

holesale

Transport

Hotel, A

ccom

odation

Constructio

n services

Other se

rvices, n.e.s.

I(t) B

illions of 2

013 HU

F

Baseline effects Heterogenous effects by sector

Figure E.2.1: The sensitivity of the estimated aggregate program e�ect (in billions of 2013HUF) to adding sectoral heterogeneity

45